共查询到20条相似文献,搜索用时 15 毫秒
1.
Tom Braden Anthony Licata Nicholas Proudfoot Ben Webster 《Advances in Mathematics》2010,225(4):2002-2049
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 of our algebras, which are in many ways analogous to integral blocks of category O. 相似文献
2.
We extend the theory of chiral and factorization algebras, developed for curves by Beilinson and Drinfeld (American Mathematical
Society Colloquium Publications, 51. American Mathematical Society, Providence, RI, 2004), to higher-dimensional varieties. This extension entails the development of the homotopy theory of chiral and factorization
structures, in a sense analogous to Quillen’s homotopy theory of differential graded Lie algebras. We prove the equivalence
of higher-dimensional chiral and factorization algebras by embedding factorization algebras into a larger category of chiral
commutative coalgebras, then realizing this interrelation as a chiral form of Koszul duality. We apply these techniques to
rederive some fundamental results of Beilinson and Drinfeld (American Mathematical Society Colloquium Publications, 51. American
Mathematical Society, Providence, RI, 2004) on chiral enveloping algebras of *{\star} -Lie algebras. 相似文献
3.
We extend the bar–cobar adjunction to operads and properads, not necessarily augmented. Due to the default of augmentation, the objects of the dual category are endowed with a curvature. As usual, the bar–cobar construction gives a cofibrant resolution for any properad. Applied to the properad encoding unital and counital Frobenius algebras, notion which appears in 2d-TQFT, it defines the associated notion up to homotopy. We further define a curved Koszul duality theory for operads or properads presented with quadratic, linear and constant relations. This provides smaller resolutions. We apply this new theory to study the homotopy theory and the cohomology theory of unital associative algebras. 相似文献
4.
Let \(X\) be a partial flag variety, stratified by orbits of the Borel. We give a criterion for the category of modular perverse sheaves to be equivalent to modules over a Koszul ring. This implies that modular category \(\mathcal O\) is governed by a Koszul-algebra in small examples. 相似文献
5.
Bruno Vallette 《Transactions of the American Mathematical Society》2007,359(10):4865-4943
The notion of prop models the operations with multiple inputs and multiple outputs, acting on some algebraic structures like the bialgebras or the Lie bialgebras. In this paper, we generalize the Koszul duality theory of associative algebras and operads to props.
6.
Tom Braden 《Transactions of the American Mathematical Society》2007,359(1):385-415
We show that certain categories of perverse sheaves on affine toric varieties and defined by dual cones are Koszul dual in the sense of Beilinson, Ginzburg and Soergel (1996). The functor expressing this duality is constructed explicitly by using a combinatorial model for mixed sheaves on toric varieties.
7.
Let and be dual Koszul algebras. By Positselski a filtered algebra with gr is Koszul dual to a differential graded algebra . 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.
9.
We show that Verdier duality for certain sheaves on the moduli spaces of graphs associated to differential graded operads corresponds to the cobar-duality of operads (which specializes to Koszul duality for Koszul operads). This in particular gives a conceptual explanation of the appearance of graph cohomology of both the commutative and Lie types in computations of the cohomology of the outer automorphism group of a free group. Another consequence is an explicit computation of dualizing sheaves on spaces of metric graphs, thus characterizing to which extent these spaces are different from oriented orbifolds. We also provide a relation between the cohomology of the space of metric ribbon graphs, known to be homotopy equivalent to the moduli space of Riemann surfaces, and the cohomology of a certain sheaf on the space of usual metric graphs. 相似文献
10.
11.
For affine toric varieties X and defined by dual cones, we define an equivalence of categories between mixed versions of the equivariant derived category and the derived category of sheaves on which are locally constant with unipotent monodromy on each orbit. This equivalence satisfies the Koszul duality formalism of Beilinson, Ginzburg, and Soergel. 相似文献
12.
We define and investigate a class of Koszul quasi-hereditary algebras for which there is a natural equivalence between the bounded derived category of graded modules and the bounded derived category of graded modules over (a proper version of) the extension algebra of standard modules. Examples of such algebras include, in particular, the multiplicity free blocks of the BGG category O, and some quasi-hereditary algebras with Cartan decomposition in the sense of König. 相似文献
13.
Dag Oskar Madsen 《Advances in Mathematics》2011,(6):2327
We propose a new definition of Koszulity for graded algebras where the degree zero part has finite global dimension, but is not necessarily semi-simple. The standard Koszul duality theorems hold in this setting. 相似文献
14.
Volodymyr Mazorchuk 《manuscripta mathematica》2010,131(1-2):1-10
We give a complete picture of the interaction between Koszul and Ringel dualities for quasi-hereditary algebras admitting linear tilting (co)resolutions of standard and costandard modules. We show that such algebras are Koszul, that the class of these algebras is closed with respect to both dualities and that on this class these two dualities commute. All arguments reduce to short computations in the bounded derived category of graded modules. 相似文献
15.
16.
《Journal of Pure and Applied Algebra》2023,227(3):107208
We develop a curved Koszul duality theory for algebras presented by quadratic-linear-constant relations over unital versions of binary quadratic operads. As an application, we study Poisson n-algebras given by polynomial functions on a standard shifted symplectic space. We compute explicit resolutions of these algebras using curved Koszul duality. We use these resolutions to compute derived enveloping algebras and factorization homology on parallelized simply connected closed manifolds with coefficients in these Poisson n-algebras. 相似文献
17.
Boris Shoikhet 《Advances in Mathematics》2010,224(3):731-12
Let α be a quadratic Poisson bivector on a vector space V. Then one can also consider α as a quadratic Poisson bivector on the vector space V∗[1]. Fixed a universal deformation quantization (prediction of some complex weights to all Kontsevich graphs [12]), we have deformation quantization of the both algebras S(V∗) and Λ(V). These are graded quadratic algebras, and therefore Koszul algebras. We prove that for some universal deformation quantization, independent on α, these two algebras are Koszul dual. We characterize some deformation quantizations for which this theorem is true in the framework of the Tamarkin's theory [19]. 相似文献
18.
S. V. Lapin 《Mathematical Notes》2013,94(3-4):335-350
The notion of differential Lie module over a curved coalgebra is introduced. The homotopy invariance of the structure of a differential Liemodule over a curved coalgebra is proved. A relationship between the homotopy theory of differential Lie modules over curved coalgebras and the theory of Koszul duality for quadratic-scalar algebras over commutative unital rings is determined. 相似文献
19.
We study the so-called weakly Koszul modules and characterise their Koszul duals. We show that the (adjusted) associated graded module of a weakly Koszul module exactly determines the homology modules of the Koszul dual. We give an example of a quasi-Koszul module which is not weakly Koszul. 相似文献