Hopf-cyclic cohomology of quantum enveloping algebras

Atabey Kaygun; Serkan Sütlü

doi:10.4171/JNCG/238

Hopf-cyclic cohomology of quantum enveloping algebras

Atabey Kaygun, Serkan Sütlü

Department of Mathematics Engineering

Isik University

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

2 Citations (Scopus)

Abstract

In this paperwe calculate both the periodic and non-periodic Hopf-cyclic cohomology of Drinfeld-Jimbo quantum enveloping algebra U_q.g/ for an arbitrary semi-simple Lie algebra g with coefficients in a modular pair in involution. We obtain this result by showing that the coalgebra Hochschild cohomology of these Hopf algebras are concentrated in a single degree determined by the rank of the Lie algebra g.

Original language	English
Pages (from-to)	429-446
Number of pages	18
Journal	Journal of Noncommutative Geometry
Volume	10
Issue number	2
DOIs	https://doi.org/10.4171/JNCG/238
Publication status	Published - 2016

Bibliographical note

Publisher Copyright:
© European Mathematical Society.

Keywords

Hopf-cyclic cohomology
Noncommutative geometry
Quantum enveloping algebra
Quantum groups

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10.4171/JNCG/238

Cite this

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title = "Hopf-cyclic cohomology of quantum enveloping algebras",

abstract = "In this paperwe calculate both the periodic and non-periodic Hopf-cyclic cohomology of Drinfeld-Jimbo quantum enveloping algebra Uq.g/ for an arbitrary semi-simple Lie algebra g with coefficients in a modular pair in involution. We obtain this result by showing that the coalgebra Hochschild cohomology of these Hopf algebras are concentrated in a single degree determined by the rank of the Lie algebra g.",

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AU - Sütlü, Serkan

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N2 - In this paperwe calculate both the periodic and non-periodic Hopf-cyclic cohomology of Drinfeld-Jimbo quantum enveloping algebra Uq.g/ for an arbitrary semi-simple Lie algebra g with coefficients in a modular pair in involution. We obtain this result by showing that the coalgebra Hochschild cohomology of these Hopf algebras are concentrated in a single degree determined by the rank of the Lie algebra g.

AB - In this paperwe calculate both the periodic and non-periodic Hopf-cyclic cohomology of Drinfeld-Jimbo quantum enveloping algebra Uq.g/ for an arbitrary semi-simple Lie algebra g with coefficients in a modular pair in involution. We obtain this result by showing that the coalgebra Hochschild cohomology of these Hopf algebras are concentrated in a single degree determined by the rank of the Lie algebra g.

KW - Hopf-cyclic cohomology

KW - Noncommutative geometry

KW - Quantum enveloping algebra

KW - Quantum groups

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Hopf-cyclic cohomology of quantum enveloping algebras

Abstract

Bibliographical note

Keywords

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