论文标题
在$τ$上 - 使用多项式增长的对称代数的有限性
On $τ$-tilting finiteness of symmetric algebras of polynomial growth
论文作者
论文摘要
在本文中，我们报告了$τ$在代数封闭的字段上的某些有限维代数的有限性，包括多项式增长的对称代数，$ 0 $ -HECKE代数和$ 0 $ -SCHUR代数。因此，我们发现衍生的等效性保留了$τ$在多项式增长的对称代数上的有限性，而多项式生长的自注射蜂窝代数为$τ$是有限的。此外，表示代表性和$τ$ - 超过$ 0 $ -HECKE代数和$ 0 $ -Schur代数（除了少数例外）的有限性。
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.
