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Mutating signed $\tau$-exceptional sequences

Part of: Representation theory of rings and algebras

Published online by Cambridge University Press:  12 October 2023

Aslak Bakke Buan Open the ORCID record for Aslak Bakke Buan [Opens in a new window]  and
Bethany Rose Marsh
Aslak Bakke Buan*
Affiliation:
Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway.
Bethany Rose Marsh
Affiliation:
School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK.
*
Corresponding author: Aslak Bakke Buan; Email: aslak.buan@ntnu.no
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Abstract

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.

Keywords

Mutationexceptional sequencestau-tilting

MSC classification

Primary: 16G10: Representations of Artinian rings
Secondary: 16G20: Representations of quivers and partially ordered sets

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 65 , Issue 3 , September 2023 , pp. 716 - 729
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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Footnotes

Dedicated to the memory of Helmut Lenzing

This work was supported by FRINAT grant number 301375 from the Norwegian Research Council. This work was partially supported by a grant from the Simons Foundation. The authors would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Cluster Algebras and Representation Theory where work on this paper was undertaken. Both authors would like to thank the Centre of Advanced Study, Oslo for support and hospitality during the programme Representation Theory: Combinatorial Aspects and Applications.

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