Some algebraic structures connected with the Yang-Baxter equation. Representations of quantum algebras

From MaRDI portal
Publication:791939

DOI10.1007/BF01076718zbMath0536.58007WikidataQ59722109 ScholiaQ59722109MaRDI QIDQ791939

Evgueni K. Sklyanin

Publication date: 1983

Published in: Functional Analysis and its Applications (Search for Journal in Brave)




Related Items

The rational Sklyanin algebra and the Wilson and para-Racah polynomialsOn Yang-Baxter equation and Calabi-Yau property of Koszul algebrasUnnamed Item\(R\)-matrix quantization of the elliptic Ruijsenaars-Schneider modelIntegrable \(N\)-dimensional systems on the Hopf algebra and \(q\)-deformationsThe four-dimensional Sklyanin algebrasReflection positivity for the complementary series of SL(2n, \({\mathbb{C}})\)Introduction to the theory of elliptic hypergeometric integralsAn algebra arising from 2-state chiral Potts model and Sklyanin algebraModules over the 4-dimensional Sklyanin algebraAn elliptic quantum algebra for \(\widehat{\text{sl}}_ 2\)Analytic theory of the eight-vertex modelAn elementary approach to \(6j\)-symbols (classical, quantum, rational, trigonometric, and elliptic)Matrix factorization for solutions of the Yang-Baxter equationHypergroups and hypergroup algebrasNew elliptic solutions of the Yang-Baxter equationDifference operators of Sklyanin and van Diejen type.Spectral duality in elliptic systems, six-dimensional gauge theories and topological stringsProperties of kernels of integral equations in XXZ models of arbitrary spinClassical limits of the SU(2)-invariant solutions of the Yang-Baxter equationGeneric algebras with quadratic commutation relationsGröbner-Shirshov basis and minimal projective resolution of \(U_q^+(A_{n})\)The structure relation for Askey-Wilson polynomialsThree dimensional Sklyanin algebras and Gröbner basesElliptic Racah polynomialsOn the equivalence of two fundamental theta identitiesEigenvalues of Ruijsenaars–Schneider models associated with An−1 root system in Bethe ansatz formalismConstruction of \(\theta\)-Poincaré algebras and their invariants on \(\mathcal M_{\theta}\)Little and big \(q\)-Jacobi polynomials and the Askey-Wilson algebraIntegrable many-body systems in the field theoriesQuantum transfer matrices for discrete and continuous quasi-exactly solvable problemsOn matrix representations of deformed Lie algebras for quantized HamiltoniansTheq-Onsager algebra and multivariableq-special functionsSome exceptional compact matrix pseudogroupsA categorical approach to dynamical quantum groupsClassical integrable systems and soliton equations related to eleven-vertex \(R\)-matrixFinite-dimensional representations of the elliptic modular doubleA class of AS-regular algebras of dimension five.The star-triangle relation, lens partition function, and hypergeometric sum/integrals\(U_{\mathfrak{q}}\mathfrak{sl}_2 \)-invariant non-compact boundary conditions for the XXZ spin chainL-operator for Belavin’s R-matrix acting on the space of theta functionsIntertwining operators for Sklyanin algebra and elliptic hypergeometric seriesIrreducible representations of the quantum analogue of SU(2)Homological properties of certain generalized Jacobian Poisson structures in dimension 3Noncommutative curves and noncommutative surfacesVertex operators, solvable lattice models and metaplectic Whittaker functionsThe quantum group SLq⋆(2) and quantum algebra Uq(sl2⋆) based on a new associative multiplication on 2 × 2 matricesOn the elliptic 𝔤𝔩2 solid-on-solid model: Functional relations and determinantsIntegrability of a family of quantum field theories related to sigma modelsHomological properties of sklyanin algebrasFlat periodic representations of \({\mathcal U}_ q({\mathcal G})\)The hyperbolic moduli space of flat connections and the isomorphism of symplectic multiplicity spacesOn algebras of skew polynomials generated by quadratic homogeneous relations.Integer solutions of integral inequalities and \(H\)-invariant Jacobian Poisson structuresThermodynamics of the quantumsu(1, 1) Landau–Lifshitz modelYang-Baxter \(\mathcal R\)-operators and parameter permutationsSklyanin-like algebras for (q-)linear grids and (q-)para-Krawtchouk polynomialsMaps from Feigin and Odesskii's elliptic algebras to twisted homogeneous coordinate ringsQuantum transfer-matrices for the sausage modelDouble Ore extensions.Coherent states for quantum compact groupsQuantum affine algebras and holonomic difference equationsPoisson geometry and representations of PI 4-dimensional Sklyanin algebrasExotic elliptic algebras of dimension 4. With an appendix by Derek TomlinQuartic Poisson algebras and quartic associative algebras and realizations as deformed oscillator algebrasSurface defects and elliptic quantum groupsMacdonald polynomials from Sklyanin algebras: A conceptual basis for the \(p\)-adics-quantum group connectionRegularity of Algebras Related to the Sklyanin AlgebraQUASITRIANGULAR HOPF ALGEBRAS, BRAID GROUPS AND QUANTUM ENTANGLEMENTSuperpotentials and higher order derivations.On quantum integrability of the Landau–Lifshitz modelMultidimensional residues and polynomial equationsLarge commutative subalgebras of quantum algebras.Double extension regular algebras of type (14641).Poisson (co)homology of polynomial Poisson algebras in dimension four: Sklyanin's caseOn factorized Lax pairs for classical many-body integrable systemsNoncommutative finite dimensional manifolds. II: Moduli space and structure of noncommutative 3-spheresGeneralized Lamé functions. I. The elliptic caseA geometric invariant of 6-dimensional subspaces of 4×4 matricesLens elliptic gamma function solution of the Yang–Baxter equation at roots of unityContinuous biorthogonality of an elliptic hypergeometric functionOn the Hochschild homology of elliptic Sklyanin algebras.Unnamed ItemAlgebra of symmetries of three-frequency hyperbolic resonanceAlgebraic Bethe ansatz for the elliptic quantum group \(E_{\tau,\eta} (sl_2\))Normalizing extensions of the two-Veronese of a three dimensional Artin-Schelter regular algebra on two generatorsAlgebra of functions on the quantum group SU(2)Elliptic Kac-Sylvester matrix from difference Lamé equationAlgebraic integrability of the two-body Ruijsenaars operator\(Q\)-operators for higher spin eight vertex models with a rational anisotropy parameterCoherent states for the quantum complex planeDeformations of \(W\)-algebras associated to simple Lie algebrasComments on all-loop constraints for scattering amplitudes and Feynman integralsThe vertex-face correspondence and the elliptic \(6j\)-symbolsHigher charges and regularized quantum trace identities in su(1,1) Landau–Lifshitz modelLeft-covariant first order differential calculus on quantum Hopf supersymmetry algebraBraided matrix structure of the Sklyanin algebra and of the quantum Lorentz groupField analogue of the Ruijsenaars-Schneider modelComposition of kinetic momenta: The \({\mathcal U}_ q(sl(2))\) caseCyclic monodromy matrices for \(sl(n)\) trigonometric \(R\)-matricesRoots of unity: Representations for symplectic and orthogonal quantum groupsOdd supersymmetrization of elliptic R-matricesDegenerate Sklyanin algebras, Askey–Wilson polynomials and Heun operators\(Q\)-operators for higher spin eight vertex models with an even number of sitesNon relativistic limit of integrable QFT with fermionic excitations




This page was built for publication: Some algebraic structures connected with the Yang-Baxter equation. Representations of quantum algebras