Related papers: Modular Koszul duality for Soergel bimodules

We study a natural enlargement of the BGG Category O for a semisimple Lie algebra: the category of weight modules with trivial central character and finite-dimensional weight spaces supported on the root lattice. We give a geometric…

We investigate the problem when the tensor functor by a bimodule yields a singular equivalence. It turns out that this problem is equivalent to the one when the Hom functor given by the same bimodule induces a triangle equivalence between…

We show that various combinatorial invariants of matroids such as Chow rings and Orlik--Solomon algebras may be assembled into "operad-like" structures. Specifically, one obtains several operads over a certain Feynman category which we…

A well-known and old result of Hazewinkel and Koszul states that the cohomology of a finite-dimensional Lie algebra is isomorphic, up to a suitable shift, to its twisted homology, a Lie-theoretical version of Poincare duality. This paper…

Let $A$ be a graded algebra. In this paper we develop a generalized Koszul theory by assuming that $A_0$ is self-injective instead of semisimple and generalize many classical results. The application of this generalized theory to directed…

We develop the basic constructions of homological algebra in the (appropriately defined) unbounded derived categories of modules over algebras over coalgebras over noncommutative rings (which we call semialgebras over corings). We define…

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. We prove a Koszul duality theory for PROPs generalizing the one for…

In this paper, we define $A_{\infty}$-Koszul duals for directed $A_{\infty}$-categories in terms of twists in their $A_{\infty}$-derived categories. Then, we compute a concrete formula of $A_{\infty}$-Koszul duals for path algebras with…

Let V be a holomorphic bundle over a complex manifold M, and s be a holomorphic section of V. We study different types of cohomology associated to the Koszul complex induced by s. When M is complete, these cohomologies are isomorphic to…

This paper investigates the representation-theoretic structure of the Koszul cohomology of a smooth projective variety $X$ over an algebraically closed field $k$, admitting an action of a finite group $G$ of order coprime to ${\rm…

Given an elementary simple-minded collection in the derived category of a non-positive dg algebra with finite-dimensional total cohomology, we construct a silting object via Koszul duality.

Let $W$ be an affine Weyl group, and let $\Bbbk$ be a field of characteristic $p>0$. The diagrammatic Hecke category $\mathcal{D}$ for $W$ over $\Bbbk$ is a categorification of the Hecke algebra for $W$ with rich connections to modular…

We discuss the notion of Poincar\'e duality for graded algebras and its connections with the Koszul duality for quadratic Koszul algebras. The relevance of the Poincar\'e duality is pointed out for the existence of twisted potentials…

We define an extension of the affine Brauer algebra, the type B/C affine Brauer algebra. This new algebra contains the hyperoctahedral group and it naturally acts on $END_K(X \otimes V^{\otimes k})$ for Orthogonal and Symplectic groups.…

In this paper we construct, for F_1 and F_2 subbundles of a vector bundle E, a "Koszul duality" equivalence between derived categories of G_m-equivariant coherent (dg-)sheaves on the derived intersection of F_1 and F_2 inside E, and the…

We introduce the alternating Schur algebra $AS_F(n,d)$ as the commutant of the action of the alternating group $A_d$ on the $d$-fold tensor power of an $n$-dimensional $F$-vector space. When $F$ has characteristic different from $2$, we…

In this paper we express certain multiplicities in modular representation-theoretic categories of type A in terms of affine p-Kazhdan-Lusztig polynomials. The representation-theoretic categories we deal with include the categories of…

Let $V$ be a free module of rank $n$ over a commutative unital ring $k$. We prove that tensor space $V^{\otimes r}$ satisfies Schur--Weyl duality, regarded as a bimodule for the action of the group algebra of the Weyl group of…

I review the proposal of Berenstein-Douglas for a completely general definition of Seiberg duality. To give evidence for their conjecture I present the first example of a physical dual pair and explicitly check that it satisfies the…

It is shown that the idempotent completion of the additive hull of the tensor product of the residue category of the category of paths of a locally finite quiver modulo an admissible ideal and a dualizing category is dualizing. Furthermore,…