Multiparameter quantum function algebra at roots of 1

DOI10.1007/BF01445276zbMath0858.16035arXivhep-th/9410106OpenAlexW2025556285MaRDI QIDQ2563775

Michela Varagnolo, Mauro Costantini

Publication date: 17 March 1997

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9410106

zbMATH Keywords

Hopf algebrasdualitydimensionrepresentationsPoisson manifoldsCartan torussimple algebraic groupssymplectic leavesmultiparameter deformationsquantum function algebrasskew endomorphisms

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Representation theory for linear algebraic groups (20G05) Lie algebras of vector fields and related (super) algebras (17B66) Deformations of associative rings (16S80)

Related Items (12)

On the Quantum Function Algebra at Roots of One ⋮ Algebraic structure of multiparameter quantum groups ⋮ A Littlewood-Richardson filtration at roots of 1 for quantum deformations of skew Schur modules ⋮ Simple modules over the multiparameter quantum function algebra at roots of 1 ⋮ Poisson orders on large quantum groups ⋮ Quantum subgroups of simple twisted quantum groups at roots of one ⋮ PBW-bases of coideal subalgebras and a freeness theorem ⋮ A class of quadratic matrix algebras arising from the quantized enveloping algebra Uq(A2n−1) ⋮ Hopf algebras of type \(A_n\), twistings and the FRT-construction. ⋮ Twisted deformations vs. cocycle deformations for quantum groups ⋮ Multiparameter quantum groups at roots of unity ⋮ Two-parameter quantum deformation of Lie superalgebras

Cites Work

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• Quantum groups at roots of 1
• Algebras of functions on compact quantum groups, Schubert cells and quantum tori
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Quantum deformations of certain simple modules over enveloping algebras
• Poisson Lie groups, dressing transformations, and Bruhat decompositions
• Quantum function algebra at roots of 1
• Multiparameter quantum groups and twisted quasitriangular Hopf algebras
• Matched pairs of groups and bismash products of hopf algebras
• Quantum Coadjoint Action
• Quantum double and multiparameter quantum groups
• On the Decomposition of Orthogonalities into Symmetries

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