Related papers: Reconstruction Algebras of Type D (II)
This paper concerns preprojective representations of a finite connected valued quiver without oriented cycles. For each such representation, an explicit formula in terms of the geometry of the quiver gives a unique, up to a certain…
We examine how generalised geometries can be associated with a labelled Dynkin diagram built around a gravity line. We present a series of new generalised geometries based on the groups $\mathit{Spin}(d,d)\times\mathbb{R}^+$ for which the…
Given any Koszul algebra of finite global dimension one can define a new algebra, which we call a higher zigzag algebra, as a twisted trivial extension of the Koszul dual of our original algebra. If our original algebra is the path algebra…
Lie quasi-bialgebras are natural generalisations of Lie bialgebras introduced by Drinfeld. To any Lie quasi-bialgebra structure of finite-dimensional (G, \mu, \gamma ,\phi ?), correspond one Lie algebra structure on D = G\oplus G*, called…
We prove a number of results on the structure and representation theory of the rational Cherednik algebra of the imprimitive reflection group $G(\ell,p,n)$. In particular, we: (1) show a relationship to the Coulomb branch construction of…
We characterize pairs (Q,d) consisting of a quiver Q and a dimension vector d, such that over a given algebraically closed field k there are infinitely many representations of Q of dimension vector d. We also present an application of this…
We give a presentation of localized affine and degenerate affine Hecke algebras of arbitrary type in terms of weights of the polynomial subalgebra and varied Demazure-BGG type operators. We offer a definition of a graded algebra…
We use a geometric description of $m$-cluster categories of Dynkin type $A$ to count the the number of coloured quivers in the $m$-mutation class of quivers of Dynkin type $A$. This is related to angulations of polygons and the cell-growth…
We first prove that the K-theoretic Hall algebra of a preprojective algebra of affine type is isomorphic to the positive half of a quantum toroidal quantum group. An essential step consists to deform the K-theoretic Hall algebra so that the…
The quantum double $D(G)=\Bbb C(G)\rtimes \Bbb C G$ of a finite group plays an important role in the Kitaev model for quantum computing, as well as in associated TQFT's, as a kind of Poincar\'e group. We interpret the known construction of…
For any acyclic quiver, we establish a family of structure isomorphisms for its cohomological Hall algebra (CoHA). The family is parameterized by partitions of the quiver into Dynkin subquivers. For each such partition, we write the domain…
We introduce a multivariate generalization of normalized Chebyshev polynomials of the second kind. We prove that these polynomials arise in the context of cluster characters associated to Dynkin quivers of type $\mathbb A$ and…
In this article, we show the relation between the irreducible idempotents of the cyclic group algebra $\mathbb F_qC_n$ and the central irreducible idempotents of the group algebras $\mathbb F_qD_{2n}$, where $\mathbb F_q$ is a finite field…
We define a new type of Hall algebras associated e.g. with quivers with polynomial potentials. The main difference with the conventional definition is that we use cohomology of the stack of representations instead of constructible sheaves…
This is a noncommutative-geometric study of the semiclassical dynamics of finite topological D-brane systems. Starting from the formulation in terms of A -infinity categories, I show that such systems can be described by the noncommutative…
The concept of modulation is generalized to pseudo-modulation and its subclasses including pre-modulation, generalized modulation and regular modulation. The motivation is to define the valued analogue of natural quiver, called {\em natural…
Let G be a Lie group and Q a quiver with relations. In this paper, we define G-valued representations of Q which directly generalize G-valued representations of finitely generated groups. Although as G-spaces, the G-valued quiver…
The first part of these notes is devoted to an introduction to algebraic $D$-modules. Several basic notions are introduced. In the second part, $D$-modules with group action are treated. Several important examples in this situation are…
We introduce an analogue of the $q$-Schur algebra associated to Coxeter systems of type $\hat A_{n-1}$. We give two constructions of this algebra. The first construction realizes the algebra as a certain endomorphism algebra arising from an…
The irreducible components of varieties parametrizing the finite dimensional representations of a finite dimensional algebra $\Lambda$ are explored, with regard to both their geometry and the structure of the modules they encode. Provided…