Singular equivalences of trivial extensions

TL;DR

This paper establishes a triangle equivalence between the singularity categories of trivial extension algebras derived from a specific pair of bimodules over artin algebras, with implications and examples provided.

Contribution

It introduces a novel method to relate singularity categories of trivial extensions via bimodule-induced triangle equivalences.

Findings

Proves a triangle equivalence between singularity categories of trivial extensions.

Provides consequences and an illustrative example.

Enhances understanding of singularity categories in algebra.

Abstract

We prove that a certain pair of bimodules over two artin algebras gives rise to a triangle equivalence between the singularity categories of the two corresponding trivial extension algebras. Some consequences and an example are given.