Stable Projective Homotopy Theory of Modules,Tails, and Koszul Duality |
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Authors: | Roberto Martínez Villa |
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Affiliation: | Instituto de Mathemáticas , Universidad Nacional Autonoma de Mexico , Morelia, Mich., Mexico |
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Abstract: | A contravariant functor is constructed from the stable projective homotopy theory of finitely generated graded modules over a finite-dimensional algebra to the derived category of its Yoneda algebra modulo finite complexes of modules of finite length. If the algebra is Koszul with a noetherian Yoneda algebra, then the constructed functor is a duality between triangulated categories. If the algebra is self-injective, then stable homotopy theory specializes trivially to stable module theory. In particular, for an exterior algebra the constructed duality specializes to (a contravariant analog of) the Bernstein–Gelfand–Gelfand correspondence. |
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Keywords: | Koszul duality Stable homotopy theory of modules Tails Totally linear complex Weakly Koszul |
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