Gorenstein derived categories

By Nan Gao, Pu Zhang. 2010

103 citations recorded by the source corpus.

Abstract Gorenstein derived categories are defined, and the relation with the usual derived categories is given. The bounded Gorenstein derived categories of Gorenstein rings and of finite-dimensional algebras are explicitly described via the homotopy categories of Gorenstein-projective modules, and some applications are obtained. Gorenstein derived equivalences between CM-finite Gorenstein algebras are discussed.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c6cfba19ad6b29f63a0d9cf2dbadee3c93f6b285

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In Algebra and Number Theory

1. Xiao-Wu Chen
2. Pu Zhang
3. Xiu-Hua Luo
4. Apostolos Beligiannis
5. Chrysostomos Psaroudakis
6. Nan Gao
7. P. Ara
8. Kulumani M. Rangaswamy

In Geometry and Topology

1. Xiao-Wu Chen
2. Pu Zhang
3. Xiu-Hua Luo
4. Apostolos Beligiannis
5. Chrysostomos Psaroudakis
6. Nan Gao
7. P. Ara
8. Kulumani M. Rangaswamy

In Statistical and Nonlinear Physics

1. Xiao-Wu Chen
2. Pu Zhang
3. Xiu-Hua Luo
4. Chrysostomos Psaroudakis
5. Nan Gao
6. Apostolos Beligiannis

Citations in the corpus

• Gorenstein Homological Algebra of Artin Algebras (2017, background): “ closed under taking direct summands. Denote by Σ GP the class of all the right GP-quasi-isomorphisms in K(A-Mod); it is a saturated multiplicative system. The following is initiated by Gao and Zhang [31]; also see [22]. Definition 3.3.1. The Gorenstein-projective derived category D GP(A) of an artin”
• Homotopy Equivalences induced by Balanced Pairs (2008, background): “Note that Buan considers relative derived categories in quite a different setup [5, Section 2], and Gorenstein derived categories in the sense of Gao and Zhang are examples of relative derived categories [15].”
• Monic representations and Gorenstein-projective modules (2011, background): “This class of modules enjoys more stable properties than the usual projective modules (see [Auslander and Bridger 1969], where it was called a module of G-dimension zero); it becomes a main ingredient in the relative homological algebra [Enochs and Jenda 1995; 2000] and in the representation theory ”
• Monomorphism categories, cotilting theory, and Gorenstein-projective modules (2011, background): “ry 11.5.3). Determining all the Cohen-Macaulay A-modules and all the Gorenstein-projective A-modules in explicit way, is a basic requirement in applications (see e.g. [AM], [B], [BGS], [CPST], [EJ2], [GZ], [K]). Corollary 4.1. (i) Let Abe an Artin algebra with inj.dimAA<∞. Then CM(Tn(A)) = Sn(CM(”