关于 band 模与 $\tau$-倾斜有限性
表示论
2020-12-22 v4 环与代数
摘要
本文受 Brauer-Thrall 猜想的 -倾斜版本启发，研究有限维代数模范畴中 band 模及其自同态的一般性质。作为应用，我们描述了含 band 模的挠类的性质。进一步，我们证明一个特殊双序列代数是 -倾斜有限的当且仅当没有 band 模是砖。我们还重新得到了用 Brauer 图刻画 Brauer 图代数 -倾斜有限性的判据。
引用
@article{arxiv.1911.09021,
title = {On band modules and $\tau$-tilting finiteness},
author = {Sibylle Schroll and Hipolito Treffinger and Yadira Valdivieso},
journal= {arXiv preprint arXiv:1911.09021},
year = {2020}
}
备注
To appear in Mathematische Zeitschrift. Substantial re-write: introduced tau-tilting version of the Brauer-Thrall conjectures for finite dimensional algebras and proof of the conjectures for special biserial algebras; removed Proposition 3.1 which contained a mistake; new proof of the criterion of tau-tilting finiteness for special biserial algebras