Journal of Homotopy and Related Structures

, Volume 12, Issue 3, pp 549–576 | Cite as

A characteristic map for compact quantum groups

  • Atabey Kaygun
  • Serkan SütlüEmail author


We show that if G is a compact Lie group and \(\mathfrak {g}\) is its Lie algebra, then there is a map from the Hopf-cyclic cohomology of the quantum enveloping algebra \(U_q(\mathfrak {g})\) to the twisted cyclic cohomology of quantum group algebra \({\mathcal O}(G_q)\). We also show that the Schmüdgen-Wagner index cocycle associated with the volume form of the differential calculus on the standard Podleś sphere \({\mathcal O}(S^2_q)\) is in the image of this map.


Compact quantum group algebra Characteristic map Cyclic cohomology 



We would like to thank the anonymous referee whose careful reading and numerous suggestions greatly improved mathematical content and exposition of the article. We are grateful to the referee for alerting us about the existence of the unpublished note [27].


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© Tbilisi Centre for Mathematical Sciences 2016

Authors and Affiliations

  1. 1.Department of MathematicsIstanbul Technical UniversityIstanbulTurkey
  2. 2.Department of MathematicsIşık UniversityIstanbulTurkey

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