# $\tau$-exceptional sequences

@article{Buan2018tauexceptionalS, title={\$\tau\$-exceptional sequences}, author={Aslak Bakke Buan and Bethany Rose Marsh}, journal={arXiv: Representation Theory}, year={2018} }

We introduce the notions of $\tau$-exceptional and signed $\tau$-exceptional sequences for any finite dimensional algebra. We prove that for a fixed algebra of rank $n$, and for any positive integer $t \leq n$, there is a bijection between the set of such sequences of length $t$, and (basic) ordered support $\tau$-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…

## 3 Citations

### Counting the Number of τ-Exceptional Sequences over Nakayama Algebras

- MathematicsAlgebras and Representation Theory
- 2021

The notion of a τ-exceptional sequence was introduced by Buan and Marsh in (2018) as a generalisation of an exceptional sequence for finite dimensional algebras. We calculate the number of complete…

### A Category of Wide Subcategories

- MathematicsInternational Mathematics Research Notices
- 2019

An algebra is said to be $\tau$-tilting finite provided it has only a finite number of $\tau$-rigid objects up to isomorphism. To each such algebra, we associate a category whose objects are the…

### Silting objects.

- Mathematics
- 2018

We give an overview of recent developments in silting theory. After an introduction on torsion pairs in triangulated categories, we discuss and compare different notions of silting and explain the…

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The class of support $\tau$-tilting modules was introduced recently by Adachi, Iyama and Reiten. These modules complete the class of tilting modules from the point of view of mutations. Given a…

### A Category of Wide Subcategories

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An algebra is said to be $\tau$-tilting finite provided it has only a finite number of $\tau$-rigid objects up to isomorphism. To each such algebra, we associate a category whose objects are the…

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