Tau-tilting modules over trivial extenstions

TL;DR

This paper investigates support tau-tilting modules over trivial extensions of finite-dimensional algebras, extending previous results on triangular matrix rings by constructing new classes via adjoint functors.

Contribution

It introduces two new classes of support tau-tilting modules over trivial extensions, generalizing prior work on triangular matrix rings using adjoint functors.

Findings

Constructed two classes of support tau-tilting modules

Extended and generalized results on triangular matrix rings

Provided new methods for studying tau-tilting modules

Abstract

We study (support) $\tau$-tilting modules over the trivial extensions of finite dimensional algebras. More precisely, we construct two classes of (support)$\tau$-tilting modules in terms of the adjoint functors which extend and generalize the results on (support) $\tau$-tilting modules over triangular matrix rings given by Gao-Huang.