An approximate equivalence for the GNS representation of the Haar state of SUq(2)

Authors

Partha Sarathi Chakraborty, Indian Statistical Institute, Kolkata
Arup Kumar Pal, Indian Statistical Institute (Delhi Centre)

Article Type

Research Article

Publication Title

Indian Journal of Pure and Applied Mathematics

Abstract

We use the crystallised C^∗-algebra C(SUq(2)) at q=0 to obtain a unitary that gives an approximate equivalence involving the GNS representation on the L² space of the Haar state of the quantum SU(2) group and the direct integral of all the infinite dimensional irreducible representations of the C∗-algebra C(SUq(2)) for nonzero values of the parameter q. This approximate equivalence gives a KK class via the Cuntz picture in terms of quasihomomorphisms as well as a Fredholm representation of the dual quantum group SUq(2)^ with coefficients in a C^∗-algebra in the sense of Mishchenko.

First Page

879

Last Page

892

DOI

10.1007/s13226-024-00633-0

Publication Date

9-1-2024

Recommended Citation

Chakraborty, Partha Sarathi and Pal, Arup Kumar, "An approximate equivalence for the GNS representation of the Haar state of SUq(2)" (2024). Journal Articles. 4594.
https://digitalcommons.isical.ac.in/journal-articles/4594