Differential Calculi over Quantum Groups and Twisted Cyclic Cocycles

2001/10/18 by Johan Kustermans, J. Kustermans, Gerard J. Murphy +6
Mathematics · #46L #81R50 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:46L #msc:81R50

paper · pdf · doi:10.48550/arxiv.math/0110199

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openalex publication_date 2001/10/18 · arxiv created 2001/10/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study some aspects of the theory of non-commutative differential calculi over complex algebras, especially over the Hopf algebras associated to compact quantum groups in the sense of S.L. Woronowicz. Our principal emphasis is on the theory of twisted graded traces and their associated twisted cyclic cocycles. One of our principal results is a new method of constructing differential calculi, using twisted graded traces.

Citations

• Differential calculus on compact matrix pseudogroups (quantum groups)

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