Three lectures on quantum groups: Representations, duality, real forms

DOI10.1016/0393-0440(93)90065-MzbMath0786.17009MaRDI QIDQ687753

Vladimir K. Dobrev

Publication date: 15 May 1994

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

zbMATH Keywords

surveyquantum groupsreal formsdual Hopf algebrasirreducible subquotients2- parameter deformation of \(GL(2)\)algebraic aspectsVerma modules of quantized enveloping algebras

Mathematics Subject Classification ID

Related Items (2)

From the Wigner–Eckart theorem to the Hilbert–Schmidt scalar product for an adjoint representation of the quantum algebra Up,q(su2) ⋮ Maps between deformed and ordinary gauge fields

Cites Work

• Multiparameter associative generalizations of canonical commutation relations and quantized planes
• Some remarks on Koszul algebras and quantum groups
• q-Weyl group and a multiplicative formula for universal R-matrices
• An analogue of P.B.W. theorem and the universal R-matrix for \(U_ h\mathfrak{sl}(N+1)\)
• On quantum groups
• Quantum inverse problem method. I
• Some algebraic structures connected with the Yang-Baxter equation
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
• Compact matrix pseudogroups
• Quantum deformations of certain simple modules over enveloping algebras
• Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra
• Multiparametric quantum deformation of the general linear supergroup
• Yang-Baxter equation and representation theory. I
• Universal \(R\)-matrix for quantized (super)algebras
• Singular vectors of quantum group representations for straight Lie algebra roots
• Decomposition theorem for Hopf algebras and pro-affine algebraic groups
• Multiparameter quantum groups and twisted quasitriangular Hopf algebras
• Some aspects of quantum groups and supergroups
• Diagonalisation of GL(N) invariant transfer matrices and quantum N-wave system (Lee model)
• QUASITRIANGULAR HOPF ALGEBRAS AND YANG-BAXTER EQUATIONS
• REPRESENTATIONS OF QUANTUM GROUPS AT ROOTS OF 1: REDUCTION TO THE EXCEPTIONAL CASE
• Duality for the matrix quantum group GLp,q(2,C)
• Canonical q-deformations of noncompact Lie (super-)algebras
• The antipode of and star operations in a Hopf algebra
• The spectral theory of a functional-difference operator in conformal field theory
• Lie superalgebras
• Covariant differential calculus on the quantum hyperplane
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Three lectures on quantum groups: Representations, duality, real forms