A note on singular equivalences and idempotents

Abstract

Let $\Lambda$ be an Artin algebra and let $e$ be an idempotent in $\Lambda$. We study certain functors which preserve the singularity categories. Suppose $\mathrm{pd}\Lambda e_{e\Lambda e}<\infty$ and ${\mathrm{id}}_{\Lambda }\frac{\Lambda /⟨e⟩}{\mathrm{rad}\Lambda /⟨e⟩}<\infty$, we show that there is a singular equivalence between $e\Lambda e$ and $\Lambda$.

6 pages

References in corpus (1)

• Triangulated categories of singularities and D-branes in Landau-Ginzburg models