Quantum group actions on rings and equivariant K-theory

zbMATH Open1331.19005arXiv0912.3569MaRDI QIDQ5416231

R. B. Zhang, Gus I. Lehrer

Publication date: 19 May 2014

Abstract: Let $Uq$ be a quantum group. Regarding a (noncommutative) space with $Uq$-symmetry as a $Uq$-module algebra $A$, we may think of equivariant vector bundles on $A$ as projective $A$-modules with compatible $Uq$-action. We construct an equivariant K-theory of such quantum vector bundles using Quillen's exact categories, and provide means for its compution. The equivariant K-groups of quantum homogeneous spaces and quantum symmetric algebras of classical type are computed.

Full work available at URL: https://arxiv.org/abs/0912.3569

zbMATH Keywords

quantum homogeneous spacesequivariant \(K\)-theoryquantum symmetric algebrasquantum universal enveloping algebraquantum group action

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) Geometry of quantum groups (58B32) Quantum groups (quantized function algebras) and their representations (20G42) Equivariant (K)-theory (19L47)

Related Items (2)

Affine quantum groups and equivariant \(K\)-theory ⋮ Title not available (Why is that?)

This page was built for publication: Quantum group actions on rings and equivariant K-theory

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q5416231)