On $τ$-tilting finiteness of symmetric algebras of polynomial growth
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866913482208706560 |
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| author | Miyamoto, Kengo Wang, Qi |
| author_facet | Miyamoto, Kengo Wang, Qi |
| contents | In this paper, we report on the $τ$-tilting finiteness of some classes of finite-dimensional algebras over an algebraically closed field, including symmetric algebras of polynomial growth, $0$-Hecke algebras and $0$-Schur algebras. Consequently, we find that derived equivalence preserves the $τ$-tilting finiteness over symmetric algebras of polynomial growth, and self-injective cellular algebras of polynomial growth are $τ$-tilting finite. Furthermore, the representation-finiteness and $τ$-tilting finiteness over $0$-Hecke algebras and $0$-Schur algebras (with few exceptions) coincide. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_03079 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On $τ$-tilting finiteness of symmetric algebras of polynomial growth Miyamoto, Kengo Wang, Qi Representation Theory Rings and Algebras In this paper, we report on the $τ$-tilting finiteness of some classes of finite-dimensional algebras over an algebraically closed field, including symmetric algebras of polynomial growth, $0$-Hecke algebras and $0$-Schur algebras. Consequently, we find that derived equivalence preserves the $τ$-tilting finiteness over symmetric algebras of polynomial growth, and self-injective cellular algebras of polynomial growth are $τ$-tilting finite. Furthermore, the representation-finiteness and $τ$-tilting finiteness over $0$-Hecke algebras and $0$-Schur algebras (with few exceptions) coincide. |
| title | On $τ$-tilting finiteness of symmetric algebras of polynomial growth |
| topic | Representation Theory Rings and Algebras |
| url | https://arxiv.org/abs/2207.03079 |