On $\tau$-tilting modules over trivial extensions of gentle tree algebras

Qi Wang; Yingying Zhang

On $\tau$-tilting modules over trivial extensions of gentle tree algebras

Representation Theory 2025-03-14 v2

Authors: Qi Wang , Yingying Zhang

Abstract

We show that trivial extensions of gentle tree algebras are exactly Brauer tree algebras without exceptional vertex. We also give a characterization for the algebras whose trivial extensions are Brauer line/star/cycle algebras. As a consequence, the number of support $\tau$ -tilting modules over the trivial extension $T(A)$ of a gentle tree algebra $A$ depends only on the number of simple $A$ -modules.

Keywords

tau-tilting modules gentle tree algebras trivial extensions brauer tree algebras support tau-tilting

Cite

@article{arxiv.2204.06418,
  title  = {On $\tau$-tilting modules over trivial extensions of gentle tree algebras},
  author = {Qi Wang and Yingying Zhang},
  journal= {arXiv preprint arXiv:2204.06418},
  year   = {2025}
}

Comments

13 pages, accepted for publication in Kodai Mathematical Journal

On $\tau$-tilting modules over trivial extensions of gentle tree algebras

Abstract

Keywords

Cite

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