Related papers: Note On The Algebraic Irregular Riemann-Hilbert Co…

For every semi-simple Lie algebra one can construct the Drinfeld-Jimbo algebra U. This algebra is a deformation Hopf algebra defined by generators and relations. To study the representation theory of U, Drinfeld used the KZ-equations to…

We give an explicit formula for the correspondence between simple Yetter-Drinfeld modules for certain finite-dimensional pointed Hopf algebras $H$ and those for cocycle twists $H^{\sigma}$ of $H$. This implies an equivalence between modules…

We construct a moduli scheme for semistable pre-$\D$-modules with prescribed singularities and numerical data on a smooth projective variety. These pre-$\D$-modules are to be viewed as regular holonomic $\D$-modules with `level structure'.…

In the work of Hoshino, Kato and Miyachi, the authors look at t-structures induced by a compact object, C, of a triangulated category, T, which is rigid in the sense of Iyama and Yoshino. Hoshino, Kato and Miyachi show that such an object…

We construct a weak representation of the category of framed affine tangles on a disjoint union of triangulated categories ${\mathcal D}_{2n}$. The categories we use are that of coherent sheaves on Springer fibers over a nilpotent element…

The aim of this paper is to study the structures of split regular Hom-Lie Rinehart algebras. Let $(L,A)$ be a split regular Hom-Lie Rinehart algebra. We first show that $L$ is of the form $L=U+\sum_{[\gamma]\in\Gamma/\thicksim}I_{[\gamma]}$…

We show that the bounded derived category of regular holonomic D-modules on a smooth variety is equivalent to the homotopy catgory of compact (or constructible) modules over the motivic ring spectrum $H_{dR}$ representing algebraic de Rham…

We introduce and study a category of algebras strongly connected with the structure of the Gelfand-Tsetlin subalgebras of the endomorphism algebras of Bott-Samelson bimodules. We develop a series of techniques that allow us to obtain…

It is a well established fact that the notions of quasi-abelian categories and tilting torsion pairs are equivalent. This equivalence fits in a wider picture including tilting pairs of $t$-structures. Firstly, we extend this picture into a…

This paper studies the intersections of Hecke correspondences on the modular varieties of $\mathcal{D}$ -elliptic sheaves in the higher-rank setting, where $\mathcal{D}$ is a "maximal order" in a central division algebra $D$ over a global…

The purpose of this work is to define a derived Hall algebra $\mathcal{DH}(T)$, associated to any dg-category $T$ (under some finiteness conditions). Our main theorem states that $\mathcal{DH}(T)$ is associative and unital. It is shown that…

We relate the Algebra of the Infrared of Gaiotto-Moore-Witten with the theory of perverse schobers which are (conjectural, in general) categorical analogs of perverse sheaves. A perverse schober on a complex plane C can be seen as an…

We prove that, for a proper connective dg algebra $A$ with cohomology concentrated in degrees between $1-d$ and $0$, the extended heart $\mathcal{D}^{fd}(A)^{(-d,0]}\subseteq \mathcal{D}^{fd}(A)$ is an extriangulated category with…

Let $\mathbf{G}$ be a connected reductive group over an algebraically closed field $\mathbb{F}$ of good characteristic, satisfying some mild conditions. In this paper we relate tilting objects in the heart of Bezrukavnikov's exotic…

For a Grothendieck category C which, via a Z-generating sequence (O(n))_{n in Z}, is equivalent to the category of "quasi-coherent modules" over an associated Z-algebra A, we show that under suitable cohomological conditions "taking…

We introduce the class of split regular Hom-Leibniz algebras as the natural generalization of split Leibniz algebras and split regular Hom-Lie algebras. By developing techniques of connections of roots for this kind of algebras, we show…

We show that every higher Auslander algebra $A_{n+1}^d$ of type $\mathbb{A}$ such that $\gcd(n,d)=1$ is derived equivalent to a certain replicated algebra $B=B_0^{(n+d)}$. Moreover ${\rm{gldim}} B = nd$ and $B$ admits an $nd$-cluster…

Representations of $C^*$-algebras are realized on section spaces of holomorphic homogeneous vector bundles. The corresponding section spaces are investigated by means of a new notion of reproducing kernel, suitable for dealing with…

Given a grading by an abelian group G on a semisimple Lie algebra L over an algebraically closed field of characteristic 0, we classify up to isomorphism the simple objects in the category of finite-dimensional G-graded L-modules. The…

Recollements of abelian categories are used as a basis of a homological and recursive approach to quasi-hereditary algebras. This yields a homological proof of Dlab and Ringel's characterisation of idempotent ideals occuring in heredity…