Related papers: Graded super duality for general linear Lie supera…
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…
Considering the general linear Lie superalgebra $\mathfrak{gl}(m|n)=\mathfrak{gl}(m|n)_{\bar{\bar 0}}\oplus \mathfrak{gl}(m|n)_{\bar{\bar 1}}$ over $\mathbb{C}$, we first formulate a super version of Vust theorem associated with a principal…
Reflexive dg categories were introduced by Kuznetsov and Shinder to abstract the duality between bounded and perfect derived categories. In particular this duality relates their Hochschild cohomologies, autoequivalence groups, and…
Let $\Lambda = \left[\begin{array}{cc} A & 0 \\ M & B \end{array}\right] $ be an Artin algebra and $_BM_A$ a $B$-$A$-bimodule. We prove that there is a triangle equivalence $D_{sg}(\Lambda) \cong D_{sg}(A)\coprod D_{sg}(B)$ between the…
We prove uniqueness of the essential order for stratified algebras having simple preserving duality, generalizing a recent result of Coulembier for quasi-hereditary algebras. We apply this to classify, up to equivalence, regular integral…
In this paper we establish Koszul duality between dg categories and a class of curved coalgebras, generalizing the corresponding result for dg algebras and conilpotent curved coalgebras. We show that the normalized chain complex functor…
We prove a Koszul duality theorem between the category of weight modules over the quantized Coulomb branch (as defined by Braverman, Finkelberg and Nakajima) attached to a group $G$ and representation $V$ and a category of $G$-equivariant…
Graded bundles are a class of graded manifolds which represent a natural generalisation of vector bundles and include the higher order tangent bundles as canonical examples. We present and study the concept of the linearisation of graded…
We give a combinatorial model structure to the category of, not necessarily conilpotent, differential graded (dg) cocommutative coalgebras and an $\infty$-category structure to the category of curved Lie algebras over an algebraically…
Consider a pair of $S$-dual hyperspherical varieties $G\circlearrowright X$ and $G^\vee\circlearrowright X^\vee$ equipped with equivariant quantizations $Q(X)$, $Q(X^\vee)$. Assume that the local conjecture of Ben-Zvi, Sakellaridis and…
We study the notion of duality in the context of graded manifolds. For graded bundles, somehow like in the case of Gelfand representation and the duality: points vs. functions, we obtain natural dual objects which belongs to a different…
We develop a new approach to highest weight categories $\cal{C}$ with good (and cogood) posets of weights via pseudocompact algebras by introducing ascending (and descending) quasi-hereditary pseudocompact algebras. For $\cal{C}$ admitting…
Koenig and Xi introduced {\em affine cellular algebras}. Kleshchev and Loubert showed that an important class of {\em infinite dimensional} algebras, the KLR algebras $R(\Gamma)$ of finite Lie type $\Gamma$, are (graded) affine cellular; in…
The algebras of the title are infinite-dimensional graded Lie algebras $L= \bigoplus_{i=1}^{\infty}L_i$, over a field of positive characteristic $p$, that are generated by an element of degree $1$ and an element of degree $p$, and satisfy…
We establish a canonical basis character formula for the irreducible modules in arbitrary parabolic BGG-type categories, including the category of finite-dimensional modules, for finite $W$-superalgebras of type $A$. These categories…
We construct a "Koszul duality" equivalence relating the (diagrammatic) Hecke category attached to a Coxeter system and a given realization to the Hecke category attached to the same Coxeter system and the dual realization. This extends a…
The classical Stone duality associates to each Boolean algebra a topological space consisting of ultrafilters. Lawson's generalisation constructs a dual equivalence of categories of Boolean inverse $\land$-semigroups and Hausdorff ample…
We show that the blocks of category O for the Lie superalgebra q_n associated to half-integral weights carry the structure of a tensor product categorification for the infinite rank Kac-Moody algebra of type C. This allows us to prove two…
On one hand, together with Pelle Steffens, we recently characterized the infinity category of derived manifolds up to equivalence by a universal property. On the other hand, it is shown in recent work of Behrend-Liao-Xu that the category of…
The paper is dedicated to the study of certain non commutative graded AS Gorenstein algebras $\Lambda $. The main result of the paper is that for Koszul algebras $\Lambda $ with Yoneda algebra $\Gamma $, such that both $\Lambda $ and…