A characteristic map for compact quantum groups

Atabey Kaygun; Serkan Sütlü

doi:10.1007/s40062-016-0138-y

A characteristic map for compact quantum groups

Atabey Kaygun, Serkan Sütlü^*

^*Corresponding author for this work

Department of Mathematics Engineering

Isik University

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

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 Schmüdgen-Wagner index cocycle associated with the volume form of the differential calculus on the standard Podleś sphere O(Sq2) is in the image of this map.

Original language	English
Pages (from-to)	549-576
Number of pages	28
Journal	Journal of Homotopy and Related Structures
Volume	12
Issue number	3
DOIs	https://doi.org/10.1007/s40062-016-0138-y
Publication status	Published - 1 Sept 2017

Bibliographical note

Publisher Copyright:
© 2016, Tbilisi Centre for Mathematical Sciences.

Keywords

Characteristic map
Compact quantum group algebra
Cyclic cohomology

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10.1007/s40062-016-0138-y

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AB - 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 Uq(g) to the twisted cyclic cohomology of quantum group algebra O(Gq). We also show that the Schmüdgen-Wagner index cocycle associated with the volume form of the differential calculus on the standard Podleś sphere O(Sq2) is in the image of this map.

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KW - Compact quantum group algebra

KW - Cyclic cohomology

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A characteristic map for compact quantum groups

Abstract

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