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τ-tilting Finiteness of Biserial Algebras

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Abstract

We compare the notions of τ-tilting finiteness and representation-finiteness of the biserial algebras. In particular, we treat the minimal representation-infinite biserial algebras and give a full classification of them with respect to τ-tilting finiteness. We build upon Ringel’s work on minimal representation-infinite algebras and use the brick-τ-rigid correspondence of Demonet, Iyama and Jasso. As a byproduct, we obtain that a minimal representation-infinite biserial algebra is τ-tilting infinite if and only if it is a gentle algebra.

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Acknowledgements

The author would like to thank Hugh Thomas and Charles Paquette for several stimulating discussions and useful comments. Moreover, the author is grateful to the referee for various helpful comments which noticeably improved the exposition of this paper.

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  1. Queen’s University, Kingston, Canada

    Kaveh Mousavand

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Mousavand, K. τ-tilting Finiteness of Biserial Algebras. Algebr Represent Theor 26, 2485–2522 (2023). https://doi.org/10.1007/s10468-022-10170-1

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