Symmetric invariant cocycles on the duals of q-deformations

Abstract

We prove that for q not a nontrivial root of unity any symmetric invariant 2-cocycle for a completion of Uq(g) is the coboundary of a central element. Equivalently, a Drinfeld twist relating the coproducts on completions of Uq(g) and U(g) is unique up to coboundary of a central element. As an application we show that the spectral triple we defined in an earlier paper for the q-deformation of a simply connected semisimple compact Lie group G does not depend on any choices up to unitary equivalence.

18 pages; minor changes, to appear in AIM

References in corpus (1)

• The Dirac operator on compact quantum groups

Cited by in corpus (8)

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• Relations in quantized function algebras
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• On Dirac Operators and Spectral Geometry of Compact Quantum Groups
• Covariant Dirac Operators on Quantum Groups