A note on singular equivalences and idempotents

2020/01/14 by Dawei Shen, Shen, Dawei
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.RA #math.RT #msc:16G10 #msc:18E30

paper · pdf · doi:10.48550/arxiv.2001.04614

6 pages

arxiv created 2020/01/14 · arxiv updated 2020/01/15

Abstract

Let Λ be an Artin algebra and let e be an idempotent in Λ. We study certain functors which preserve the singularity categories. Suppose pdΛe_eΛe<∞ and id_Λ\tfracΛ/⟨ e⟩radΛ/⟨ e⟩ < ∞, we show that there is a singular equivalence between eΛe and Λ.

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