Gorenstein derived categories

Gao, Nan; Zhang, Pu

doi:10.1016/j.jalgebra.2010.01.027

Cited by 78 publications

(44 citation statements)

References 23 publications

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“…The bounded Gorenstein derived category of mod-A, denoted by D b Gp (mod-A), is the Verdier quotient category K b (mod-A)/K b Gp-ac (mod-A). This notion introduced by Gao and Zhang [20]. Then, this category has been studied more in [3] and [2].…”

Section: Recollements and Gorenstein Derived Categoriesmentioning

confidence: 99%

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On the Recollements of Functor Categories

Asadollahi

Hafezi

Vahed

2015

Appl Categor Struct

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This paper is devoted to the study of recollements of functor categories in different levels. In the first part of the paper, we start with a small category S and a maximal object s of S and construct a recollement of Mod-S in terms of Mod-End S (s) and Mod-(S \ {s}) in four different levels. In case S is a finite directed category, by iterating this argument, we get chains of recollements having some interesting applications. In the second part, we start with a recollement of rings and construct a recollement of their path rings, with respect to a finite quiver. Third part of the paper presents some applications, including recollements of triangular matrix rings, an example of a recollement in Gorenstein derived level and recollements of derived categories of N -complexes.

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Section: Recollements and Gorenstein Derived Categoriesmentioning

confidence: 99%

“…The notion of Gorenstein derived category was first introduced by Gao and Zhang [20]. In the second subsection of the last section, we give a Gorenstein derived level recollement of a path algebra.…”

Section: Introductionmentioning

confidence: 99%

On the Recollements of Functor Categories

Asadollahi

Hafezi

Vahed

2015

Appl Categor Struct

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“…Recall from [11] For our second main theorem we need a definition and some lemmas. Recall from [18] that a full subcategory B of a compactly generated triangulated category T is smashing if the inclusion B → T has a right adjoint which preserves coproducts.…”

Section: Theorem 22 Let a Be A Virtually Gorenstein Artin Algebra Ofmentioning

confidence: 99%

A Smashing Subcategory of the Homotopy Category of Gorenstein Projective Modules

Gao

2013

Appl Categor Struct

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Let A be an artin algebra of finite CM-type. In this paper, we show that if A is virtually Gorenstein, then the homotopy category of Gorenstein projective A-modules, denote K(A-GP), is always compactly generated. Based on this result, it will be proved that the homotopy category of projective A-modules, denote K(A-P), is a smashing subcategory of K(A-GP) and the corresponding Verdier quotient is also compactly generated. Furthermore, it turns out that the inclusion functor i : K(A-P) → K(A-GP) induces a recollement of K(A-GP).

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“…Enochs extended their ideas and introduced Gorenstein projective, Gorenstein injective and Gorenstein flat modules and correspondent dimensions over arbitrary rings, see the book [9] for details. Later Gorenstein homogical theory was extensively studied and developed by Avromov, Martsinkovsky, Christensen, Veliche, Sather-Wagstaff, Chen, Beligiannis, Yang and many others (see for instance [3,4,7,8,10,12,13,14] etc. ).…”

Section: Introductionmentioning

confidence: 99%