Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence
نویسندگان
چکیده
منابع مشابه
Koszul Duality and Equivalences of Categories
Let A and A! be dual Koszul algebras. By Positselski a filtered algebra U with grU = A is Koszul dual to a differential graded algebra (A!, d). We relate the module categories of this dual pair by a⊗−Hom adjunction. This descends to give an equivalence of suitable quotient categories and generalizes work of Beilinson, Ginzburg, and Soergel.
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Given a hyperplane arrangement in an affine space equipped with a linear functional, we define two finite-dimensional, noncommutative algebras, both of which are motivated by the geometry of hypertoric varieties. We show that these algebras are Koszul dual to each other, and that the roles of the two algebras are reversed by Gale duality. We also study the centers and representation categories ...
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Koszul algebras have arisen in many contexts; algebraic geometry, combinatorics, Lie algebras, non-commutative geometry and topology. The aim of this paper and several sequel papers is to show that for any finite dimensional algebra there is always a naturally associated Koszul theory. To obtain this, the notions of Koszul algebras, linear modules and Koszul duality are extended to additive (gr...
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ژورنال
عنوان ژورنال: Memoirs of the American Mathematical Society
سال: 2011
ISSN: 0065-9266,1947-6221
DOI: 10.1090/s0065-9266-2010-00631-8