A Uniqueness Property of $\tau $-Exceptional Sequences

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2023-08-16 DOI:10.1007/s10468-023-10226-w

Eric J. Hanson, Hugh Thomas

引用次数: 0

Abstract

Recently, Buan and Marsh showed that if two complete $\tau $-exceptional sequences agree in all but at most one term, then they must agree everywhere, provided the algebra is $\tau $-tilting finite. They conjectured that the result holds without that assumption. We prove their conjecture. Along the way, we also show that the dimension vectors of the modules in a $\tau $-exceptional sequence are linearly independent.

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$$\tau $$ -例外序列的唯一性

最近，布安和马什证明，如果两个完整的（\tau \）例外序列除了最多一个项之外都一致，那么只要代数是（\tau \）倾斜有限的，它们一定在所有地方都一致。他们猜想，如果没有这个假设，结果也是成立的。我们证明了他们的猜想。同时，我们还证明了在$\tau $-例外序列中模块的维向量是线性独立的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebras and Representation Theory 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups. The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.

A Uniqueness Property of \(\tau \)-Exceptional Sequences

Abstract