Abstract
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 \(A\mbox{-}\)modules, denote \(K(A\mbox{-}{\mathcal {GP}})\), is always compactly generated. Based on this result, it will be proved that the homotopy category of projective \(A\mbox{-}\)modules, denote \(K(A\mbox{-}{\mathcal P})\), is a smashing subcategory of \(K(A\mbox{-}{\mathcal {GP}})\) and the corresponding Verdier quotient is also compactly generated. Furthermore, it turns out that the inclusion functor \(i: K(A\mbox{-}{\mathcal P})\to K(A\mbox{-}{\mathcal {GP}})\) induces a recollement of \(K(A\mbox{-}{\mathcal {GP}})\).
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Supported by the National Natural Science Foundation of China (Grant No. 11101259).
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Gao, N. A Smashing Subcategory of the Homotopy Category of Gorenstein Projective Modules. Appl Categor Struct 23, 87–91 (2015). https://doi.org/10.1007/s10485-013-9325-8
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DOI: https://doi.org/10.1007/s10485-013-9325-8