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tau-tilting

Glasgow Mathematical Journal (1)

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Mutating signed $\tau$-exceptional sequences
Part of
- Representation theory of rings and algebras
Aslak Bakke Buan, Bethany Rose Marsh
Journal:

Glasgow Mathematical Journal / Volume 65 / Issue 3 / September 2023

Published online by Cambridge University Press:

12 October 2023, pp. 716-729

Print publication:

September 2023
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We establish some properties of $\tau$-exceptional sequences for finite-dimensional algebras. In an earlier paper, we established a bijection between the set of ordered support $\tau$-tilting modules and the set of complete signed $\tau$-exceptional sequences. We describe the action of the symmetric group on the latter induced by its natural action on the former. Similarly, we describe the effect on a $\tau$-exceptional sequence obtained by mutating the corresponding ordered support $\tau$-tilting module via a construction of Adachi-Iyama-Reiten.