Related papers: Borel and shifted category O

In this paper new equivalence relations on the category $Mod(A)$ for any associative algebra $A$ and several related results are given. The new equivalence relations are defined using restrictions to subalgebras and the action of algebra…

We bound the Borel cardinality of the isomorphism relation for nuclear simple separable C*-algebras: It is turbulent, yet Borel reducible to the action of the automorphism group of the Cuntz algebra O_2 on its closed subsets. The same…

We study the category O of representations over a shifted Yangian. This category has a tensor product structure and contains distinguished modules, the positive prefundamental modules and the negative prefundamental modules. Motivated by…

The notion of crossed modules for Lie 2-algebras is introduced. We show that, associated to such a crossed module, there is a strict Lie 3-algebra structure on its mapping cone complex and a strict Lie 2-algebra structure on its…

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…

We construct a 2-category associated with a Kac-Moody algebra and we study its 2-representations. This generalizes earlier work with Chuang for type A. We relate categorifications relying on K_0 properties and 2-representations.

Let $A$ be a hereditary algebra. We construct a fundamental domain for the cluster category of $A$ inside the category of modules over the duplicated algebra $\bar{A}$ of $A$. We then prove that there exists a bijection between the tilting…

We study automorphic Lie algebras and their applications to integrable systems. Automorphic Lie algebras are a natural generalisation of celebrated Kac-Moody algebras to the case when the group of automorphisms is not cyclic. They are…

In this article, we introduce a category of weak Lie 3-algebras with suitable weak morphisms. The definition is based on the construction of a partial resolution over $\mathbb{Z}$ of the Koszul dual cooperad of the $\textrm{Lie}$ operad,…

We explicitly construct families of simple modules for Lie algebras of rank $2$, on which certain commutative subalgebra acts diagonally and has a simple spectrum. In type $A$ these modules are well known generic Gelfand-Tsetlin modules and…

We prove that on a certain class of smooth complex varieties (those with "affine even stratifications"), the category of mixed Hodge modules is "almost" Koszul: it becomes Koszul after a few unwanted extensions are eliminated. We also give…

We construct a symmetric monoidal category $LIE^{MC}$ whose objects are shifted L-infinity algebras equipped with a complete descending filtration. Morphisms of this category are "enhanced" infinity morphisms between shifted L-infinity…

We develop a theory of toroidal vertex algebras and their modules, and we give a conceptual construction of toroidal vertex algebras and their modules. As an application, we associate toroidal vertex algebras and their modules to toroidal…

In this paper we study the category of braided categorical Leibniz algebras and braided crossed modules of Leibniz algebras and we relate these structures with the categories of braided categorical Lie algebras and braided crossed modules…

In this paper we consider the category $C (\tilde k, \tilde H)$ of the $(\tilde k, \tilde H)$-modules, including all the Verma modules, where $k$ is some compact Lie algebra and H some Cartan subgroup, $\tilde k$ and $\tilde H$ are the…

We prove that for a countable, commutative ring $R$, the class of countable $R$-modules either has only countably many isomorphism types, or else it is Borel complete. The machinery gives a succinct proof of the Borel completeness of TFAB,…

We classify extensions of certain classifiable C*-algebras using the six term exact sequence in K-theory together with the positive cone of the K_0-groups of the distinguished ideal and quotient. We then apply our results to a class of…

We study the finite-dimensional simple modules, over an algebraically closed field, of the affine Temperley--Lieb algebra corresponding to the affine Weyl group of type $A$. These turn out to be closely related to the simple modules for a…

We define and study an analogue of Category O in the context of Kazhdan and Laumon's gluing construction for perverse sheaves on the basic affine space. We explicitly describe the simple objects in this category, and we show its linearized…

The aim of this paper is to give relations between the category of finetely generated graded modules over the homogeneized Weyl algebra $B_{n}$, the finetely generated modules over the Weyl algebra $A_{n}$ and the finetely generated graded…