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On τ-tilting modules over trivial extensions of gentle tree algebras · arXivDesk

2204.06418Apr 13, 202213 pages, accepted for publication in Kodai Mathematical Journal

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

Qi Wang, Yingying Zhang

Representation Theory

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 $τ$ -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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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.

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The paper addresses: On τ-tilting modules over trivial extensions of gentle tree algebras.
We show that trivial extensions of gentle tree algebras are exactly Brauer tree algebras without exceptional vertex.

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Author comment: 13 pages, accepted for publication in Kodai Mathematical Journal

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