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Symmetric invariant cocycles on the duals of q-deformations |
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| Authors: | Sergey Neshveyev Lars Tuset |
| Affiliation: | aDepartment of Mathematics, University of Oslo, P.O. Box 1053 Blindern, NO-0316 Oslo, Norway;bInstitut de Mathématiques de Jussieu, Université Paris 7 Denis Dedirot, France;cFaculty of Engineering, Oslo University College, P.O. Box 4 St. Olavs plass, NO-0130 Oslo, Norway |
| Abstract: | We prove that for q∈C? not a nontrivial root of unity any symmetric invariant 2-cocycle for a completion of Uqg is the coboundary of a central element. Equivalently, a Drinfeld twist relating the coproducts on completions of Uqg and Ug 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. |
| Keywords: | Quantum groups Tensor categories Cohomology Dirac operator |
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