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On $τ$-tilting modules over trivial extensions of gentle tree algebras (2204.06418v2)
Published 13 Apr 2022 in math.RT
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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