تقرير
An approximate equivalence for the GNS representation of the Haar state of $SU_{q}(2)$
| العنوان: | An approximate equivalence for the GNS representation of the Haar state of $SU_{q}(2)$ |
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| المؤلفون: | Chakraborty, Partha Sarathi, Pal, Arup Kumar |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Operator Algebras, Mathematics - Quantum Algebra, 58B32, 46L67, 19K35 |
| الوصف: | 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. Comment: v1: 16 pages. v2: 19 pages. The first and the last section rewritten, many references added. v3: 18 pages, final version, Introduction part rewritten |
| نوع الوثيقة: | Working Paper |
| الوصول الحر: | http://arxiv.org/abs/2203.06908Test |
| رقم الانضمام: | edsarx.2203.06908 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |