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arXiv · 2204.06418

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

Qi Wang·Yingying Zhang
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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.

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BibTeXRIS

Qi Wang, Yingying Zhang. 2022-04-13. On $\tau$-tilting modules over trivial extensions of gentle tree algebras. https://doi.org/10.2996/kmj49105

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