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Singular equivalences induced by ring extensions (2403.12412v1)
Published 19 Mar 2024 in math.RT and math.RA
Abstract: Let $B \subseteq A$ be an extension of finite dimensional algebras. We provide a sufficient condition for the existence of triangle equivalences of singularity categories (resp. Gorenstein defect categories) between $A$ and $B$. This result is applied to trivial extensions, Morita rings and triangular matrix algebras to give several reduction methods on singularity categories and Gorenstein defect categories of algebras.
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