scientific article; zbMATH DE number 793872

zbMath0839.17009MaRDI QIDQ4846800

Andrew Pressley, Vyjayanthi Chari

Publication date: 7 September 1995

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras (17-02)

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1}^{(2)}\) and \(D_{n + 1}^{(2)}\) open spin chains, Quantum affine algebras and deformations of the Virasoro and \({\mathcal W}\)-algebras, Four-dimensional \(BF\) theory as a topological quantum field theory, Yangians, integrable quantum systems and Dorey's rule, Noncommutative discriminants via Poisson primes, Twist star products and Morita equivalence, Fundamental isomorphism theorems for quantum groups, Non-Levi closed conjugacy classes of \(\mathrm{SP}_q(2n)\)., Fusion basis for lattice gauge theory and loop quantum gravity, Symmetric quiver Hecke algebras and R-matrices of quantum affine algebras, Twisted derivations of Hopf algebras., Yangian symmetries and integrability of the Dirac equation with spin symmetry, The colored HOMFLYPT function is q-holonomic, Yangians and quantum loop algebras, Analytical structure of the generalized \(\lambda\)-deformation, Bimodule structure in the periodic \({\mathfrak g}\ell (1|1)\) spin chain, Basic quantizations of \(D=4\) Euclidean, Lorentz, Kleinian and quaternionic \( {\mathfrak{o}}^{\star}(4) \) symmetries, Noncommutative relativistic spacetimes and worldlines from 2 + 1 quantum (anti-)de Sitter groups, Combinatorial aspects of the quantized universal enveloping algebra of \(\mathfrak {sl}_{n+1}\), Associative Yang-Baxter equation and Fukaya categories of square-tiled surfaces, \(\mathrm{SL}(2, \mathbb{Z})\)-action for ribbon quasi-Hopf algebras, Universal K-matrix for quantum symmetric pairs, Quasi-classical limit in \(q\)-deformed systems, non-commutativity and the \(q\)-path integral., On super Yangian covariance of the triple product system, Cyclicity and \(R\)-matrices, Mixed quantum skew Howe duality and link invariants of type \(A\), Quantum Grothendieck ring isomorphisms, cluster algebras and Kazhdan-Lusztig algorithm, Equivalences between three presentations of orthogonal and symplectic Yangians, Double Bruhat cells and symplectic groupoids, J-dendriform algebras, On the Hochschild (co)homology of quantum homogeneous spaces., The crystal duality principle: from Hopf algebras to geometrical symmetries, Quantized hyperalgebras of rank 1, Monomials of \(q\) and \(q,t\)-characters for non simply-laced quantum affinizations, Verma-type modules for quantum affine Lie algebras, Kostka-Foulkes polynomials cyclage graphs and charge statistic for the root system \(C_n\), The \(\kappa\)-(A)dS quantum algebra in \((3+1)\) dimensions, Torsion free sheaves on Weierstrass cubic curves and the classical Yang-Baxter equation, Yangian symmetry of string theory on \(\mathrm{AdS}_{3} \times S^{3} \times S^{3} \times S^{1}\) with mixed 3-form flux, Quantum homogeneous spaces with faithfully flat module structures, Braiding structures on formal Poisson groups and classical solutions of the QYBE., Yangians: their representations and characters, \(q\)-difference intertwining operators and \(q\)-conformal invariant equations, The \(SU(n)_1\) WZW models. Spinon decomposition and Yangian structure, Spin-dependent extension of Calogero-Sutherland model through anyon-like representations of permutation operators, Symmetric pairs for quantized enveloping algebras, How to regularize singular vectors and kill the dynamical Weyl group, Products in Hochschild cohomology and Grothendieck rings of group crossed products., Quantum anchor: \(U_q (sl(2))\) case, Triangular matrix representations, Frobenius splitting in characteristic zero and the quantum Frobenius map, Quantum deformation of Whittaker modules and the Toda lattice., A Kohno-Drinfeld theorem for quantum Weyl groups, Symplectic leaves of complex reductive Poisson-Lie groups, \(N\)-dimensional classical integrable systems from Hopf algebras, Wheels, wheeling, and the Kontsevich integral of the unknot, Algebraic bosonisation: the case of the Dirac fermion, Toeplitz matrices and classical and \(q\)-Bessel functions, Fourier transforms on the quantum \(\text{SU}(1,1)\) group. (With an appendix by Mizan Rahman)., Quantization of inhomogeneous Lie bialgebras, Poisson morphisms and reduced affine Poisson group actions, Automatic construction of explicit R matrices for the one-parameter families of irreducible typical highest weight (\(\dot 0_m| \dot \alpha_n\)) representations of \(U_q[gl(m| n)\)], Traces in braided categories, An algorithm for computing the global basis of an irreducible \(U_q(sp_{2n})\)-module, The \(q\)-characters at roots of unity, A quantum algebraic description of D-branes on group manifolds, Quantum differential operators on the quantum plane., Socle and some invariants of quadratic Lie superalgebras, Character formulas for \(q\)-rook monoid algebras, The q-characters of minimal affinizations of type G₂ arising from cluster algebras, Homotopy relative Rota-Baxter lie algebras, triangular 𝐿_{∞}-bialgebras and higher derived brackets, TOROIDAL q-OPERS, Symmetric ordering and Weyl realizations for quantum Minkowski spaces, Correlators on the wall and sln spin chain, Simply laced root systems arising from quantum affine algebras, Characters of infinite-dimensional quantum classical groups: BCD cases, Exotic cluster structures on 𝑆𝐿_{𝑛}: the Cremmer–Gervais case, Conformal Yang–Baxter equation on Cur(sl2(C)), Lie superbialgebra structures on the Lie superalgebra C3+A and deformation of related integrable Hamiltonian systems, Cohomologies and relative Rota-Baxter-Nijenhuis structures of 3-LieRep pairs, Introduction to classical and quantum integrability, On diagonal solutions of the reflection equation, Multisymplectic structures and invariant tensors for Lie systems, Complete spectrum of quantum integrable lattice models associated to $\boldsymbol {\mathcal{U}_{q} (\widehat{gl_{n}})}$ by separation of variables, Localization of quantum biequivariantƊ-modules and q–W algebras, The finite dual of commutative-by-finite Hopf algebras, Marginal deformations and quasi-Hopf algebras, Generic triangular solutions of the reflection equation: ${U}_{q}\left(\hat{s{l}_{2}}\right)$ case, Higher-order superintegrable momentum-dependent Hamiltonians on curved spaces from the classical Zernike system, Admissible Poisson bialgebras, Affine highest weight categories and quantum affine Schur-Weyl duality of Dynkin quiver types, On the Standard Poisson Structure and a Frobenius Splitting of the Basic Affine Space, COIDEAL SUBALGEBRAS IN QUANTUM AFFINE ALGEBRAS, On webs in quantum type C, Relative Rota-Baxter operators and symplectic structures on Lie-Yamaguti algebras, Quasi-solvable lattice models for and Demazure atoms and characters, Quantized nilradicals of parabolic subalgebras of and algebras of coinvariants, Unnamed Item, A quasi-Hopf algebra for the triplet vertex operator algebra, Isomorphism between the R-matrix and Drinfeld presentations of quantum affine algebra: Type C, Monoidal categorification and quantum affine algebras, Monoidal categories and the Gerstenhaber bracket in Hochschild cohomology, Oscillator versus prefundamental representations. II. Arbitrary higher ranks, Another approach to Hom-Lie bialgebras via Manin triples, SU q (3) corepresentations and bivariate q-Krawtchouk polynomials, Positive Level, Negative Level and Level Zero, Infinitesimal quantum group from helicity in fluid mechanics, 𝒪-Operators of Loday Algebras and Analogues of the Classical Yang–Baxter Equation, A geometric q‐character formula for snake modules, Poisson bialgebras, Twisted Yangians, twisted quantum loop algebras and affine Hecke algebras of type $BC$, Auslander-Reiten theory of small half quantum groups, TWIST DEFORMATION OF DOUBLY ENLARGED NEWTON–HOOKE HOPF ALGEBRA, Tilting modules, dominant dimensions and Brauer-Schur-Weyl duality, Vertex representations of quantum N-toroidal algebras for type C, Weighted infinitesimal unitary bialgebras on free monoid algebras, On extension of classical Baer results to Poisson algebras, Yang–Baxter deformation as an $\boldsymbol {O(d,d)}$ transformation, Nonlinear quantum equations: Classical field theory, N-ENLARGED GALILEI HOPF ALGEBRA AND ITS TWIST DEFORMATIONS, GAUGE AND POINCARÉ INVARIANT REGULARIZATION AND HOPF SYMMETRIES, Rota-Baxter operators on $\mathrm{sl(2,\mathbb {C})}$ sl (2,C) and solutions of the classical Yang-Baxter equation, Transvectants, modular forms, and the Heisenberg algebra., QUASITRIANGULAR HOPF ALGEBRAS, BRAID GROUPS AND QUANTUM ENTANGLEMENT, Topological description of representations of \(U_q(sl_2)\), On boundary fusion and functional relations in the Baxterized affine Hecke algebra, An algebraic bootstrap for dimensionally reduced quantum gravity, Integrability of the \(D^2_n\) vertex models with open boundary, Target space duality. II: Applications, Brauer algebras, symplectic Schur algebras and Schur-Weyl duality, Characters of the partition algebras., A pseudo-analyzer approach to formal group laws not of operad type, Many body problems with ``spin-related contact interactions, General integrable n-level, many-mode Janes-Cummings-Dicke models and classical r-matrices with spectral parameters, Drinfeld Realization of Twisted Quantum Affine Algebras, The coradical filtration ofU_q(g)at roots of unity, Nilpotent orbits of linear and cyclic quivers and Kazhdan-Lusztig polynomials of type A, Explicit quantization of dynamical r-matrices for finite dimensional semisimple Lie algebras, Boundary non-local charges from the open spin chain, Klein–Gordon field from the XXZ Heisenberg model, LORENTZ INVARIANT AND SUPERSYMMETRIC INTERPRETATION OF NONCOMMUTATIVE QUANTUM FIELD THEORY, Poisson Polynomial Rings, Spectra of quantized hyperalgebras, Affine quantum Schur algebras at roots of unity, Quantum group symmetries and completeness for $\boldsymbol {A}_{\boldsymbol {2n}}^{\boldsymbol{(2)}}$ open spin chains, Quantum groups, Verma modules andq-oscillators: general linear case, Weighted infinitesimal unitary bialgebras, pre-Lie, matrix algebras, and polynomial algebras, A FURTHER STUDY ON NON-ABELIAN PHASE SPACES: LEFT-SYMMETRIC ALGEBRAIC APPROACH AND RELATED GEOMETRY, Quantum integrability in the lab, Computing modular data for pointed fusion categories, The Lie groupoid analogue of a symplectic Lie group, Homotopy Brunnian links and the $\kappa $-invariant, Noncommutative fields and actions of twisted Poincaré algebra, Schwinger–Dyson operators as invariant vector fields on a matrix model analog of the group of loops, Quaternionic and Poisson–Lie structures in three-dimensional gravity: The cosmological constant as deformation parameter, Unnamed Item, Generalized twist deformations of Poincaré and Galilei quantum groups, Orthogonal basis for the Shapovalov form on $U_q(\mathfrak{sl}(n + 1))$, Unnamed Item, Toward an axiomatic formulation of noncommutative quantum field theory, Pre-Lie analogues of Poisson-Nijenhuis structures and Maurer–Cartan equations, Generalizations of the classical Yang-Baxter equation and ${\mathcal O}$O-operators, Poisson–Hopf deformations of Lie–Hamilton systems revisited: deformed superposition rules and applications to the oscillator algebra, Lie bi-algebras on the non-commutative torus, Coisotropic Lie bialgebras and complementary dual Poisson homogeneous spaces, h-adic quantum vertex algebras in types B, C, D and their ϕ-coordinated modules, All noncommutative spaces of κ-Poincaré geodesics, On the classification of $3$-dimensional $F$-manifold algebras, Symmetric polynomials in the free metabelian Poisson algebras, \(Q\widetilde{Q}\)-systems for twisted quantum affine algebras, Minimal nondegenerate extensions, Twisting theory, relative Rota-Baxter type operators and \(L_\infty\)-algebras on Lie conformal algebras, \(R\)-matrix presentation of quantum affine algebra in type \(A_{2n-1}^{(2)}\), Bicrossproduct vs. twist quantum symmetries in noncommutative geometries: the case of \(\varrho\)-Minkowski, Higher order Kirillov-Reshetikhin modules for \(\mathbf{U}_q(A_{n}^{(1)})\), imaginary modules and monoidal categorification, Cohomology and deformation quantization of Poisson conformal algebras, Hopf Structure for the q-Lévy-Meixner Oscillator Algebra, New solutions to the tetrahedron equation associated with quantized six-vertex models, Transposed Poisson algebras, Novikov-Poisson algebras and 3-Lie algebras, Flat \(GL(1|1)\)-connections and fatgraphs, Shapovalov elements of classical and quantum groups, Gauge theory on twist-noncommutative spaces, q-analog qudit Dicke states, Affinizations, R-matrices and reflection functors, A proposal for 3d quantum gravity and its bulk factorization, Three-dimensional quantum gravity from the quantum pseudo-Kähler plane, Quantum symmetric conjugacy classes of non-exceptional groups, A generalization of a SIS epidemic model with fluctuations, On the structure and representation theory of \(q\)-deformed Clifford algebras, \(U^0\)-free quantum group representations, Path description for q -characters of fundamental modules in type C, String topology in three flavors, A Drinfeld-type presentation of the orthosymplectic Yangians, Hecke symmetries associated with the polynomial algebra in 3 commuting indeterminates, Khoroshkin-Tolstoy approach to quantum superalgebras, Infinite-dimensional Lie bialgebras via affinization of Novikov bialgebras and Koszul duality, The Heisenberg double of the quantum Euclidean group and its representations, Algebraic Bethe ansatz for the open XXZ spin chain with non-diagonal boundary terms via \(U_{\mathfrak{q}}\mathfrak{sl}_2\) symmetry, Braid group action on extended crystals, Non-standard quantum algebras and finite dimensional PT -symmetric systems, Pseudo-parabolic category over quaternionic projective plane, IntroSurvey of representation theory, Davydov-Yetter cohomology and relative homological algebra, Post-groups, (Lie-)Butcher groups and the Yang-Baxter equation, Non‐semisimple Levin–Wen models and Hermitian TQFTs from quantum (super)groups, Admissible Hom-Novikov-Poisson and Hom-Gelfand-Dorfman color Hom-algebras, Monoidal categorification and quantum affine algebras. II, The \(R\)-matrix presentation for the rational form of a quantized enveloping algebra, Unnamed Item, Unnamed Item, Local conserved charges in principal chiral models, Braidings of formal Poisson groups with quasitriangular dual, Algebraic construction of quantum integrable models including inhomogeneous models, Quantum groups and non-Abelian braiding in quantum Hall systems, A new aspect of representations of \(U_q(s\hat l_2)\) -- root of unity case, Loop symmetry of integrable vertex models at roots of unity, Dynamical R-matrices for Calogero models, Tannaka duality for Maschkean categories, Representations of twisted \(q\)-Yangians, New \(R\)-matrices for small quantum groups, Construction and exact solution of a nonlinear quantum field model in quasi-higher dimension, Quantized coordinate rings, PBW-type bases and \(q\)-boson algebras, TWO DESCRIPTIONS OF THE QUANTUM AFFINE ALGEBRA U_v() VIA HALL ALGEBRA APPROACH, Octo-bialgebras, Quantum octonions, YANGIANS IN INTEGRABLE FIELD THEORIES, SPIN CHAINS AND GAUGE-STRING DUALITIES, Evaluation representations of quantum affine algebras at roots of unity, Quantum integrable systems, non-skew-symmetric r-matrices and algebraic Bethe ansatz, Kazhdan-Lusztig-dual quantum group for logarithimic extensions of Virasoro minimal models, Unnamed Item, Unnamed Item, Unnamed Item, (p, q)-Rogers-Szegö Polynomial and the (p, q)-Oscillator, Tridiagonal pairs of q-Racah type, the Bockting operator ψ, and L-operators for U_q(L(sl_2)), Unnamed Item, Lie bialgebra structures on the deformative Schrödinger-Virasoro algebras, “Many-poled” r-matrix Lie algebras, Lax operators, and integrable systems, Affinization of category $\mathcal {O}$ for quantum groups, EXAMPLE OF A GROUP WHOSE QUANTUM ISOMETRY GROUP DOES NOT DEPEND ON THE GENERATING SET, An Algorithm for Computing the Global Basis of a Finite Dimensional IrreducibleU_q(so_2n+1) orU_q(so_2n)-Module, Classical r -matrices for the generalised Chern–Simons formulation of 3d gravity, Integrable perturbations of conformal field theories and Yetter-Drinfeld modules, Demazure modules and graded limits of minimal affinizations, On a Poisson homogeneous space of bilinear forms with a Poisson-Lie action, Unnamed Item, On Yangian covariance of the triple product system with the rational R-matrix, Representations of quantum affine algebras of type $B_N$, Simple vector bundles on a nodal Weierstrass cubic and quasi-trigonometric solutions of the classical Yang–Baxter equation, DEMAZURE MODULES OF LEVEL TWO AND PRIME REPRESENTATIONS OF QUANTUM AFFINE, Modifiedn-level,n− 1-mode Tavis–Cummings model and algebraic Bethe ansatz, Poisson–Hopf algebra deformations of Lie–Hamilton systems, SYMMETRIES AND INVARIANTS OF TWISTED QUANTUM ALGEBRAS AND ASSOCIATED POISSON ALGEBRAS, LEFT-SYMMETRIC BIALGEBRAS AND AN ANALOGUE OF THE CLASSICAL YANG–BAXTER EQUATION, Mathematical Renormalization in Quantum Electrodynamics via Noncommutative Generating Series, Quantum isometry groups of dual of finitely generated discrete groups and quantum groups, Poisson Hopf algebra related to a twisted quantum group, The q-linked complex Minkowski space, its real forms and deformed isometry groups, Multiresolution wavelet analysis of integer scale Bessel functions, Unnamed Item, Reflection equation and twisted Yangians, Quasi-Hermitian quantum mechanics in phase space, 6 j symbols duality relations, Generalized Gaudin spin chains, nonskew symmetric r-matrices, and reflection equation algebras, A (q,γ) analog of the W1+∞ algebra, Quantum symmetry algebras of spin systems related to Temperley–Lieb R-matrices, Nonlocal symmetries and factorized scattering, U _q (𝒢^) Heisenberg Families, ( ℛ , p , q ) $$( \mathcal {R}, p,q)$$ -Rogers–Szegö and Hermite Polynomials, and Induced Deformed Quantum Algebras, The Steinberg-Lusztig tensor product theorem, Casselman-Shalika, and LLT polynomials, Yangian doubles of classical types and their vertex representations, Generalized Gaudin systems in an external magnetic field and reflection equation algebras, A classification of 𝐻-primes of quantum partial flag varieties, Exact solution of ansu(n) spin torus, CLASSICAL MECHANICS OF MANY PARTICLES DEFINED ON CANONICALLY DEFORMED NONRELATIVISTIC SPACETIME, Quantum algebras and symplectic reflection algebras for wreath products, Quantum isometry groups and Born reciprocity in 3d gravity, Knot invariants and higher representation theory, TWISTED RINDLER SPACETIMES, Mesure de haar sur une algebra de hopf et groupes quantiques reels, The braiding for representations of q-deformed affine sl2, Unnamed Item, TWO NON-NILPOTENT LINEAR TRANSFORMATIONS THAT SATISFY THE CUBIC q-SERRE RELATIONS, Quantum deformation of the flag variety, Crystal Graphs and the Combinatorics of Young Tableaux, Gelfand–Tsetlin Bases for Classical Lie Algebras, Quantum G2 categories have property (T), A formula for the 𝑅-matrix using a system of weight preserving endomorphisms, BMW algebra, quantized coordinate algebra and type 𝐶 Schur–Weyl duality, Yangians, quantum loop algebras, and abelian difference equations, Quantum Yang-Baxter equation and constantR-matrix over Grassmann algebra, Three-term recurrence relations of minimal affinizations of type $G_2$, F_q[M₂,F_q[GL₂], andF_q[SL₂] as Quantized Hyperalgebras], A quantum octonion algebra, EXAMPLES OF DERIVATION-BASED DIFFERENTIAL CALCULI RELATED TO NONCOMMUTATIVE GAUGE THEORIES, DIFFERENT CLASSES OF QUANTUM GATES ENTANGLERS FOR MULTIPARTITE STATES, Representation theory of (modified) reflection equation algebra of $GL(m|n)$ type, The Poincaré group as a Drinfel’d double, Noncommutative (A)dS and Minkowski spacetimes from quantum Lorentz subgroups, Graded Limits of Simple Tensor Product of Kirillov–Reshetikhin Modules for, TWIST DEFORMATIONS OF NEWTON–HOOKE HOPF ALGEBRAS, Z₂-graded classicalr-matrices and algebraic Bethe ansatz: applications to integrable models of quantum optics and nuclear physics, RAINBOW STATISTICS, TWISTED QUANTUM FIELDS ON MOYAL AND WICK–VOROS PLANES ARE INEQUIVALENT, SPACETIME FROM SYMMETRY: THE MOYAL PLANE FROM THE POINCARÉ–HOPF ALGEBRA, THE HEISENBERG FAMILY FOR THE PRINCIPAL GRADING OF $U_q(\hat{\cal G})$, Quantized enveloping algebras for Borcherds superalgebras, ALTERNATIVE PROOFS OF GENERATING FUNCTIONS FOR HAHN POLYNOMIALS AND SOME APPLICATIONS, Ambidextrous objects and trace functions for nonsemisimple categories, QUANTUM GROUPS AT ROOTS OF UNITY AND MODULARITY, ALL LINK INVARIANTS FOR TWO DIMENSIONAL SOLUTIONS OF YANG–BAXTER EQUATION AND DRESSINGS, Coorbits of Quantum Homogeneous Spaces, What a Classical r-Matrix Really Is, Quantum deformation of two four-dimensional spin foam models, 𝑞-Krawtchouk polynomials as spherical functions on the Hecke algebra of type 𝐵, AN ALGEBRAIC APPROACH TO SYMMETRIC PRE-MONOIDAL STATISTICS, On the semiduals of local isometry groups in three-dimensional gravity, On reflection algebras and twisted Yangians, Nilpotent representations of classical quantum groups at roots of unity, Cocycles on a finite dimensional quotient ofu_q(sl(2)), Loop realizations of quantum affine algebras, Universal R-matrix and functional relations, Quiver varieties and finite dimensional representations of quantum affine algebras