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arXiv · 2203.06908

An approximate equivalence for the GNS representation of the Haar state of $SU_{q}(2)$

Partha Sarathi Chakraborty·Arup Kumar Pal
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Abstract

We use the crystallised $C^*$-algebra $C(SU_{q}(2))$ at $q=0$ to obtain a unitary that gives an approximate equivalence involving the GNS representation on the $L^{2}$ 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 $C(SU_{q}(2))$ 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 $\widehat{SU_q(2)}$ with coefficients in a $C^*$-algebra in the sense of Mishchenko.

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BibTeXRIS

Partha Sarathi Chakraborty, Arup Kumar Pal. 2022-03-14. An approximate equivalence for the GNS representation of the Haar state of $SU_{q}(2)$. https://arxiv.org/abs/2203.06908

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