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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2207.03079 |
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Table of 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.