Irreducible representations of the crystallization of the quantized function algebras $C(SU_{q}(n+1))$
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917807447343104 |
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| author | Giri, Manabendra Pal, Arup Kumar |
| author_facet | Giri, Manabendra Pal, Arup Kumar |
| contents | Crystallization of the $C^*$-algebras $C(SU_{q}(n+1))$ was introduced by Giri \& Pal as a $C^*$-algebra $C(SU_{0}(n+1))$ given by a finite set of generators and relations. Here we study representations of the $C^*$-algebra $C(SU_{0}(n+1))$ and prove a factorization theorem for its irreducible representations. This leads to a complete classification of all irreducible representations of this $C^*$-algebra. As an important consequence, we prove that all the irreducible representations of $C(SU_{0}(n+1))$ arise exactly as $q\to 0+$ limits of irreducible representations of $C(SU_{q}(n+1))$. We also present a few other important corollaries of the classification theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09347 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Irreducible representations of the crystallization of the quantized function algebras $C(SU_{q}(n+1))$ Giri, Manabendra Pal, Arup Kumar Operator Algebras Quantum Algebra 20G42, 46L67, 58B32 Crystallization of the $C^*$-algebras $C(SU_{q}(n+1))$ was introduced by Giri \& Pal as a $C^*$-algebra $C(SU_{0}(n+1))$ given by a finite set of generators and relations. Here we study representations of the $C^*$-algebra $C(SU_{0}(n+1))$ and prove a factorization theorem for its irreducible representations. This leads to a complete classification of all irreducible representations of this $C^*$-algebra. As an important consequence, we prove that all the irreducible representations of $C(SU_{0}(n+1))$ arise exactly as $q\to 0+$ limits of irreducible representations of $C(SU_{q}(n+1))$. We also present a few other important corollaries of the classification theorem. |
| title | Irreducible representations of the crystallization of the quantized function algebras $C(SU_{q}(n+1))$ |
| topic | Operator Algebras Quantum Algebra 20G42, 46L67, 58B32 |
| url | https://arxiv.org/abs/2402.09347 |