Homotopy Categories, Leavitt Path Algebras, and Gorenstein Projective Modules
نویسندگان
چکیده
منابع مشابه
Homotopy Categories, Leavitt Path Algebras, and Gorenstein Projective Modules
For a finite quiver without sources or sinks, we prove that the homotopy category of acyclic complexes of injective modules over the corresponding finite-dimensional algebra with radical square zero is triangle equivalent to the derived category of the Leavitt path algebra viewed as a differential graded algebra with trivial differential, which is further triangle equivalent to the stable categ...
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We introduce the notion of relative singularity category with respect to any self-orthogonal subcategory ω of an abelian category. We introduce the Frobenius category of ω-Cohen-Macaulay objects, and under some reasonable conditions, we show that the stable category of ω-Cohen-Macaulay objects is triangle-equivalent to the relative singularity category. As applications, we relate the stable cat...
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Let R be a ring with identity and C(R) denote the category of complexes of R-modules. In this paper we study the homotopy categories arising from projective (resp. injective) complexes as well as Gorenstein projective (resp. Gorenstein injective) modules. We show that the homotopy category of projective complexes over R, denoted K(Prj C(R)), is always well generated and is compactly generated p...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2014
ISSN: 1687-0247,1073-7928
DOI: 10.1093/imrn/rnu008