Linear Koszul duality
نویسندگان
چکیده
منابع مشابه
Linear Koszul Duality
In this paper we construct, for F1 and F2 subbundles of a vector bundle E, a “Koszul duality” equivalence between derived categories of Gm-equivariant coherent (dg-)sheaves on the derived intersection F1 R ∩EF2, and the corresponding derived intersection F ⊥ 1 R ∩E∗F ⊥ 2 . We also propose applications to Hecke algebras.
متن کاملLinear Koszul Duality and Affine Hecke Algebras
In this paper we prove that the linear Koszul duality equivalence constructed in a previous paper provides a geometric realization of the Iwahori-Matsumoto involution of affine Hecke algebras.
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In this paper we use linear Koszul duality, a geometric version of the standard duality between modules over symmetric and exterior algebras studied in [MR1, MR2] to give a geometric realization of the Iwahori–Matsumoto involution of affine Hecke algebras. More generally we prove that linear Koszul duality is compatible with convolution in a general context related to convolution algebras.
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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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We prove a duality for factorization homology which generalizes both usual Poincaré duality for manifolds and Koszul duality for En-algebras. The duality has application to the Hochschild homology of associative algebras and enveloping algebras of Lie algebras. We interpret our result at the level of topological quantum field theory.
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2009
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x09004357