A characteristic map for compact quantum groups
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CitationKaygun, A., & Sütlü, S. (2017). A characteristic map for compact quantum groups. Journal of Homotopy and Related Structures, 12(3), 549-576. doi:10.1007/s40062-016-0138-y
We show that if G is a compact Lie group and g is its Lie algebra, then there is a map from the Hopf-cyclic cohomology of the quantum enveloping algebra U-q(g) to the twisted cyclic cohomology of quantum group algebra O(G(q)). We also show that the Schmudgen-Wagner index cocycle associated with the volume form of the differential calculus on the standard Podles sphere O(S-q(2)) is in the image of this map.