Into Multiplier Hopf ($*$-)Graph Algebras
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909472228638720 |
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| author | Razavinia, Farrokh |
| author_facet | Razavinia, Farrokh |
| contents | This paper is concerned with the structures introduced recently by the authors of the current paper concerning the multiplier Hopf $*$-graph algebras and also the Cuntz-Krieger algebras and their relations with the $C^*$-graph algebras, and once again by using the $C^*$-graph algebra constructions associated to our toy example, to initiate our first class of examples concerning the multiplier Hopf $*$-graph algebras.
At the final part of the paper, we apply our study to the $SL(n)$ case over the field of complex numbers, and prove that $(\mathcal{O}(SL(n),Δ)$ possesses the initial requirements of being a discrete quantum group in the sense of Van Daele, and propose a direction in approaching one step further to the problem raised by Wang, asking ``if finite groups of Lie type have an analogue of $q$-deformations into finite quantum groups?''. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09787 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Into Multiplier Hopf ($*$-)Graph Algebras Razavinia, Farrokh Quantum Algebra 46L05, 46L67, 81P40, 46L55, 17B81 This paper is concerned with the structures introduced recently by the authors of the current paper concerning the multiplier Hopf $*$-graph algebras and also the Cuntz-Krieger algebras and their relations with the $C^*$-graph algebras, and once again by using the $C^*$-graph algebra constructions associated to our toy example, to initiate our first class of examples concerning the multiplier Hopf $*$-graph algebras. At the final part of the paper, we apply our study to the $SL(n)$ case over the field of complex numbers, and prove that $(\mathcal{O}(SL(n),Δ)$ possesses the initial requirements of being a discrete quantum group in the sense of Van Daele, and propose a direction in approaching one step further to the problem raised by Wang, asking ``if finite groups of Lie type have an analogue of $q$-deformations into finite quantum groups?''. |
| title | Into Multiplier Hopf ($*$-)Graph Algebras |
| topic | Quantum Algebra 46L05, 46L67, 81P40, 46L55, 17B81 |
| url | https://arxiv.org/abs/2403.09787 |