Central extensions of quantum current groups

DOI10.1007/BF01045884zbMath0692.22011MaRDI QIDQ583396

Nicolai Reshetikhin, Michaael A. Semenov-Tian-Shansky

Publication date: 1990

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

central chargedeformationscentral extensionsCasimir elementsenveloping algebras of affine Lie algebrasnoncocommutative Hopf algebrasquantum current algebraquantum current groupsSchwinger terms

Mathematics Subject Classification ID

Infinite-dimensional Lie (super)algebras (17B65) Homological methods in Lie (super)algebras (17B55) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Deformations of associative rings (16S80)

Related Items

(T*ℬ)q, q-analog of model space and the Clebsch–Gordan coefficients generating matrices, On the Heisenberg algebra associated with the rational R-matrix, \(R\)-matrix presentation of quantum affine algebra in type \(A_{2n-1}^{(2)}\), Center of the quantum affine vertex algebra associated with trigonometric R-matrix, Quantum affine vertex algebras associated to untwisted quantum affinization algebras, Isomorphism between the R-matrix and Drinfeld presentations of quantum affine algebra: Type C, A note on constructing quasi modules for quantum vertex algebras from twisted Yangians, The PBW basis of \(U_{q,\overline{q}}(\ddot{\mathfrak{gl}}_n)\), Flag integrable models and generalized graded algebras, An algebraic bootstrap for dimensionally reduced quantum gravity, An algebraic approach to form factors, Higher rank classical analogs of the Askey-Wilson algebra from the sl_N Onsager algebra, On , , , , , , and reflectionK-matrices, h-adic quantum vertex algebras in types B, C, D and their ϕ-coordinated modules, DEFORMED DOUBLE YANGIAN STRUCTURES, Quantum and braided-Lie algebras, ℏ (YANGIAN) DEFORMATION OF THE MIURA MAP AND VIRASORO ALGEBRA, Lattice analogues of \(W\)-algebras and classical integrable equations, The quantum double in integrable quantum field theory, Free boson representation of DYℏ(glN)k and DYℏ(slN)k, An elliptic quantum algebra for \(\widehat{\text{sl}}_ 2\), Unnamed Item, Recurrence relations for off-shell Bethe vectors in trigonometric integrable models, Higher Sugawara operators for the quantum affine algebras of type \(A\), Hopf algebra extension of a Zamolochikov algebra and its double, Geometric \(q\)-hypergeometric functions as a bridge between Yangians and quantum affine algebras, Hidden quantum group symmetry in the chiral model, Lattice conformal theories and their integrable perturbations, QUASITRIANGULAR WZW MODEL, Combinatorial quantization of the Hamiltonian Chern-Simons theory. II, Yangian double, R-matrix realization of two-parameter quantum affine algebra \(U_{r, s} (\hat{\mathfrak{gl}}_n)\), Gauss decomposition for quantum groups and supergroups, The Drinfeld realization of the elliptic quantum group Bq,λ(A2(2)), On the bosonization of \(L\)-operators for the quantum affine algebra \(U_ q ({\mathfrak {sl}}_ 2)\), Deformed Virasoro algebras from elliptic quantum algebras, A central extension of \(DY_{\hbar}(\mathfrak{gl}_ 2)\), Quantum doubles of Fock type and bosonization, Quantum affine algebras and deformations of the Virasoro and \({\mathcal W}\)-algebras, Folded quantum integrable models and deformed \(W\)-algebras, Isomorphism between the \(R\)-matrix and Drinfeld presentations of quantum affine algebra: types \(B\) and \(D\), Dynamical centers for the elliptic quantum algebra $ \newcommand{\elpb}[1{{{\mathcal{B}}_{q,\lambda}(\widehat{gl}_{#1})_c}} \newcommand{\e}{{\rm e}} \elpb{2}$], Algebraic structures of quantum projective field theory related to fusion and braiding. Hidden additive weight, Bethe vectors for orthogonal integrable models, Finite-dimensional irreducible representations of reflection algebra for su(1,1)q vertex model: Classification, boson–fermion realizations, and Yang–Baxterization, Rings of \(\mathbf h\)-deformed differential operators, On the \(h\)-adic quantum vertex algebras associated with Hecke symmetries, Integrable Systems, Shuffle Algebras, and Bethe Equations, Centers of generalized reflection equation algebras, Gauss coordinates vs currents for the Yangian doubles of the classical types, Creation/annihilation operators and form factors of the \(XXZ\) model, Poisson structures on the center of the elliptic algebra \(\mathcal A_{q,p}(\widehat{\text{sl}}(2)_c)\), New \(\mathcal W_{q,p}(\text{sl}(2))\) algebras from the elliptic algebra \(\mathcal A_{q,p}(\widehat{\text{sl}}(2)_c)\), Drinfeld basis and free boson representation of twisted quantum affine superalgebra \(U_ q[\text{osp}(2| 2)^{(2)}\).], Integrable open-boundary conditions for the supersymmetric \(t\)-\(J\) model. The quantum-group-invariant case, Exact solution of the \(\text{SU}_{q}(n)\)-invariant quantum spin chains, Intertwining operators for the central extension of the Yangian double., Super-Yangian double and its central extension., Reflection equation and twisted Yangians, Quasi modules for the quantum affine vertex algebra in type \(A\), Towards Drinfeld-Sokolov reduction for quantum groups, Singular vectors of quantum group representations for straight Lie algebra roots, Reflection matrices for theU_q[sl(m|n)⁽¹⁾ vertex model], Fermionic reflection matrices, The alternating presentation of \(U_q(\widehat{gl_2})\) from Freidel-Maillet algebras, Weight functions and Drinfeld currents, Quantum affine algebras and holonomic difference equations, Quantum groups in higher genus and drinfeld's new realizations method (sl2 case), Abelian current algebra and the Virasoro algebra on the lattice, Poisson-Lie T-duality of WZW model via current algebra deformation, On Drinfeld's realization of quantum affine algebras, Lattice Virasoro from lattice Kac-Moody, Quantum current algebras associated with rational \(R\)-matrix, A Heisenberg double addition to the logarithmic Kazhdan-Lusztig duality., A new current algebra and the reflection equation, L operators and Drinfeld’s generators, \(h\)-adic quantum vertex algebras associated with rational \(R\)-matrix in types \(B\), \(C\) and \(D\), On the universal weight function for the quantum affine algebra $U_q(\widehat {\mathfrak {gl}}_N)$, Drinfeld constructions of the quantum affine superalgebra Uq(gl(m/n̂)), Representations of quantum affine algebras in their \(R\)-matrix realization, Three realizations of the quantum affine algebra \(U_{q}(A_{2}^{(2)}\), REPRESENTATIONS OF REFLECTION ALGEBRAS, FRT presentation of the Onsager algebras, Integrable boundary conditions for a non-Abelian anyon chain with \(D(D_{3})\) symmetry, On the quantum affine vertex algebra associated with trigonometric \(R\)-matrix, Solutions of the Yang–Baxter equation for (n + 1) (2n + 1)-vertex models using a differential approach, Heisenberg Double ℋ(B*) as a Braided Commutative Yetter–Drinfeld Module Algebra Over the Drinfeld Double, Zamolodchikov-Faddeev algebras for Yangian doubles at level 1, Deformed \(W\)-algebras in type \(A\) for rectangular nilpotent, Elliptic quantum group \(U_{q,p}(\widehat{\mathfrak{sl}}_2)\), Hopf algebroid structure and elliptic hypergeometric series, On the second realization for the positive part of \(U_q (\widehat{sl_2})\) of equitable type, Yangian symmetry in integrable quantum gravity, Duality and quantum-algebra symmetry of the \(A^{(1)}_{\mathcal N-1}\) open spin chain with diagonal boundary fields, \(XXZ\) chain with a boundary, Bulk and boundary \(S\)-matrices for the \(\text{SU}(N)\) chain., The twisted quantum affine algebra \(U_ q(A^{(2)}_ 2)\) and correlation functions of the Izergin-Korepin model., Freidel-Maillet type presentations of \(U_q(sl_2)\), Deformations of \(W\)-algebras associated to simple Lie algebras, Poisson reduction of the lattice Kac-Moody algebra, Representation theory of Chern-Simons observables, Quantum toroidal and shuffle algebras, Higher-order Hamiltonians for the trigonometric Gaudin model, Physical phase space of the lattice Yang-Mills theory and the moduli space of flat connections on a Riemann surface, The algebra \({\mathcal A}_{\hbar,\eta}(\hat g)\) and infinite Hopf family of algebras, \(A_{n-1}^{(1)}\) reflection \(K\)-matrices, Poisson reduction of twisted Heisenberg double and finite-dimensional integrable systems, Level-one representations and vertex operators of quantum affine superalgebra Uq[gl(N̂|N)], Isomorphism of two realizations of quantum affine algebra \(U_ q(\widehat{\mathfrak{gl}}(n))\), Braided matrix structure of the Sklyanin algebra and of the quantum Lorentz group, Cyclic monodromy matrices for \(sl(n)\) trigonometric \(R\)-matrices, Trigonometric weight functions as \(K\)-theoretic stable envelope maps for the cotangent bundle of a flag variety, Origin of quantum group and its application in integrable systems., Generalizations of Poisson structures related to rational Gaudin model, An integrable vertex model and the quantum affine algebra \(U_q(\widehat{sl}(2))\) at the critical level

Cites Work

• What is a classical r-matrix?
• Quantum R matrix for the generalized Toda system
• The complex exponent of a singularity does not change along strata mu=const
• Yang-Baxter equation and representation theory. I