On singular equivalences of Morita type
TLDR
In this paper, Chen and Sun showed that singular equivalence of Morita type has some bi-joint functor properties and preserves positive degree Hochschild homology under some conditions.About:
This article is published in Journal of Algebra.The article was published on 2013-07-01 and is currently open access. It has received 44 citations till now. The article focuses on the topics: Functor & Hochschild homology.read more
Citations
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Gorenstein categories, singular equivalences and finite generation of cohomology rings in recollements
TL;DR: In this article, the authors compared an artin algebra Λ with an idempotent element a with respect to singularity categories and the finite generation condition Fg for the Hochschild cohomology.
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Singular equivalence of Morita type with level
TL;DR: In this article, the authors generalize the notion of stable equivalence of Morita type and define a singular equivalence between singular categories with level, and prove that such an equivalence can be derived from standard type equivalence.
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Singular equivalence and the (Fg) condition
TL;DR: In this paper, it was shown that singular equivalences of Morita type with level between finite-dimensional Gorenstein algebras over a field preserve the (Fg) condition.
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Singularity categories and singular equivalences for resolving subcategories
Hiroki Matsui,Ryo Takahashi +1 more
TL;DR: In this paper, the singularity category of a resolving subcategory of an abelian category is investigated and the complete intersections over which the stable categories of resolving subcategories have trivial singularity categories are the simple hypersurface singularities of type
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The singularity category of a quadratic monomial algebra
TL;DR: In this paper, the authors exploit singular equivalences between artin algebras, that are induced from certain functors between the stable module categories, called pre-triangle equivalences.
References
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Book ChapterDOI
Derived Categories of Coherent Sheaves and Triangulated Categories of Singularities
TL;DR: In this paper, the authors established an equivalence between the category of graded D-branes of type B in Landau-Ginzburg models with homogeneous superpotential W and the triangulated category of singularities of the fiber of W over zero.
Book ChapterDOI
Equivalences of Blocks of Group Algebras
TL;DR: A block algebra over O is an indecomposable summand of the algebra of a finite group over O as mentioned in this paper, where O is a complete local noetherian ring, whose field of fractions has characteristic zero and residue field has non-zero characteristic.