We introduce the notions of τ-exceptional and signed τ-exceptional sequences for any finite dimensional algebra. We prove that for a fixed algebra of rank n, and for any positive integer $t\le n$, there is a bijection between the set of signed τ-exceptional sequences of length t, and (basic) ordered support τ-rigid objects with t indecomposable direct summands. If the algebra is hereditary, our notions coincide with exceptional and signed exceptional sequences. The latter were recently introduced by Igusa and Todorov, who constructed a similar bijection in the hereditary setting.

中文翻译：

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τ -异常序列

我们为任何有限维代数引入了τ -异常和有符号τ -异常序列的概念。我们证明对于秩为n的固定代数，对于任何正整数$吨\le n$，在长度为t 的有符号τ -异常序列集和（基本）有序支持τ -刚性对象之间存在双射，其具有t 个不可分解的直接被加数。如果代数是遗传的，我们的概念与异常和有符号异常序列相吻合。后者最近由 Igusa 和 Todorov 引入，他们在遗传环境中构建了类似的双射。