相关论文: A relation between Mirkovi\'c-Vilonen cycles and m…

It is well known that the ring radical theory can be approached via language of modules. In this work, we present some generalizations of classical results from module theory, in the two-sided and graded sense. Let $\mathsf{G}$ be a group,…

We study point modules of monomial algebras associated with symbolic dynamical systems, parametrized by proalgebraic varieties which 'linearize' the underlying dynamical systems. Faithful point modules correspond to transitive sub-systems,…

We introduce a central extension of the preprojective algebra of a finite Dynkin quiver (depending on a regular weight for the corresponding root system), whose natural deformed version is flat (unlike that for the preprojective algebra).…

The theory of representations of quivers and of their preprojective algebras are reviewed. In particular, moduli spaces of representations of these algebras, quiver varieties and reflection functor are described. The proof that the…

We study the algebraic geometry and combinatorics of the central degeneration (the degeneration that shows up in local models of Shimura varieties and Gaitsgory's central sheaves) in type A. More specifically, we elucidate the central…

W-algebras of finite type are certain finitely generated associative algebras closely related to the universal enveloping algebras of semisimple Lie algebras. In this paper we prove a conjecture of Premet that gives an almost complete…

Let $\la$ be a preprojective algebra of simply laced Dynkin type $\Delta$. We study maximal rigid $\la$-modules, their endomorphism algebras and a mutation operation on these modules. This leads to a representation-theoretic construction of…

Sherman-Zelevinsky and Cerulli constructed canonically positive bases in cluster algebras associated to affine quivers having at most three vertices. Both constructions involve cluster monomials and normalized Chebyshev polynomials of the…

Let $A={\rm \mathbb{k}}Q/\mathcal{I}$ be a gentle algebra. We provide a bijection between non-projective indecomposable Gorenstein projective modules over $A$ and special recollements induced by an arrow $a$ on any full-relational oriented…

In this paper, we treat $\mathscr{D}$-modules on the basic affine space $G/U$ and their global sections for a semisimple complex algebraic group $G$. Our aim is to prepare basic results about large non-irreducible modules for the branching…

Crawley-Boevey and Shaw recently introduced a certain multiplicative analogue of the deformed preprojective algebra, which they called the multiplicative preprojective algebra. In this paper we study the moduli space of (semi)stable…

We define the associated variety $ X_{M} $ of a module $ M $ over a finite-dimensional superalgebra $ {\mathfrak g} $, and show how to extract information about $ M $ from these geometric data. $ X_{M} $ is a subvariety of the cone $ X $ of…

To a finite quiver equipped with a positive integer on each of its vertices, we associate a holomorphic symplectic manifold having some parameters. This coincides with Nakajima's quiver variety with no stability parameter/framing if the…

The main objective of this project is to determine all irreducible modules of a given modular Lie algebra. In contrast to ordinary Lie algebras, modular Lie algebras require an additional structure known as the p-mapping. The minimal…

The present paper contains two interrelated developments. First, are proposed new generalized Verma modules. They are called k-Verma modules, k\in N, and coincide with the usual Verma modules for k=1. As a vector space a k-Verma module is…

Let $\mathfrak{g}$ be a complex simple Lie algebra and $U_q(\hat{\mathfrak{g}})$ the corresponding quantum affine algebra. We prove that every irreducible finite-dimensional $U_q(\hat{\mathfrak{g}})$-module gives rise to a family of…

We compute the number of finite dimensional irreducible modules for the algebras quantizing Nakajima quiver varieties. We get a lower bound for all quivers and vectors of framing and provide an exact count in the case when the quiver is of…

Let Q be a quiver. M. Reineke and A. Hubery investigated the connection between the composition monoid, as introduced by M. Reineke, and the generic composition algebra, as introduced by C. M. Ringel, specialised at q=0. In this thesis we…

The Jacobian algebra associated to a triangulation of a closed surface $S$ with a collection of marked points $M$ is (weakly) symmetric and tame. We show that for these algebras the Auslander-Reiten translate acts 2-periodical on objects.…

We show a few basic results about moduli spaces of semistable modules over Lie algebroids. The first result shows that such moduli spaces exist for relative projective morphisms of noetherian schemes, removing some earlier constraints. The…