Related papers: Total preprojective algebras

From the viewpoint of higher dimensional Auslander-Reiten theory, we introduce a new class of finite dimensional algebras of global dimension n, which we call n-representation infinite. They are a certain analog of representation infinite…

In this article we study the properties of preprojective algebras of representation finite species. To understand the structure of a preprojective algebra, one often studies its Nakayama automorphism. A complete description of the Nakayama…

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…

We compute the minimal model for Ginzburg algebras associated to acyclic quivers $Q$. In particular, we prove that there is a natural grading on the Ginzburg algebra making it formal and quasi-isomorphic to the preprojective algebra in…

We introduce and study a new class of algebras, which we name \textit{quantum generalized Heisenberg algebras} and denote by $\mathcal{H}_q (f,g)$, related to generalized Heisenberg algebras, but allowing more parameters of freedom, so as…

Let $K$ be a fixed field. We attach to each column-finite quiver $E$ a von Neumann regular $K$-algebra $Q(E)$ in a functorial way. The algebra $Q(E)$ is a universal localization of the usual path algebra $P(E)$ associated with $E$. The…

We consider the dual space of linear groups over Dynkinian and Euclidean algebras, i.e. finite dimensional algebras derived equivalent to the path algebra of Dynkin or Euclidean quiver. We prove that this space contains an open dense subset…

There has been substantial calculational progress in the last few years for gauge theory amplitudes which involve massless four dimensional particles. One of the central ingredients in this has been the ability to keep precise track of the…

This paper is devoted to the study of Poisson superalgebras over fields of characteristic $2$. We investigate their representations, semidirect products, cohomology, formal deformations, and universal enveloping algebras. We also introduce…

We introduce the notion of ``finite general representation type'' for a finite-dimensional algebra, a property related to the ``dense orbit property'' introduced by Chindris-Kinser-Weyman. We use an interplay of geometric, combinatorial,…

We provide a topological characterization of quivers whose path algebra satisfies a polynomial identity. This class includes the oriented cycle and acyclic quivers and, in the latter case, we describe the associated T-ideal. We introduce a…

In this paper, we introduce a new generating function called $d$-polynomial for the dimensions of $\tau$-tilting modules over a given finite dimensional algebra. Firstly, we study basic properties of $d$-polynomials and show that it can be…

We generalize the geometric construction of quiver Hecke algebras from Varagnolo and Vasserot to a setup with arbitrary connected reductive groups. This corresponds to replacing quiver representations by generalized quiver representations…

Suppose that $Q$ is a finite quiver and $G\subseteq \Aut(Q)$ is a finite group, $k$ is an algebraic closed field whose characteristic does not divide the order of $G$. For any algebra $\Lambda=kQ/{\mathcal {I}}$, $\mathcal {I}$ is an…

In arXiv:1506.05880 we gave a generalization of the theory of quivers with potentials introduced by Derksen-Weyman-Zelevinsky, via completed tensor algebras over $S$-bimodules where $S$ is a finite dimensional basic semisimple algebra. In…

We determine the structure of the BPS algebra of 2-Calabi-Yau Abelian categories for which the stack of objects admits a good moduli space. We prove that this algebra is isomorphic to the positive part of the enveloping algebra of a…

Let $Q$ be a tree-type quiver, $\mathbf{k} Q$ its path algebra, and $\lambda$ a nonzero element in the field $\mathbf{k}$. We construct irreducible morphisms in the Auslander-Reiten quiver of the transjective component of the bounded…

For a commutative ring $R$ and an ADE Dynkin quiver $Q$, we prove that the multiplicative preprojective algebra of Crawley-Boevey and Shaw, with parameter $q=1$, is isomorphic to the (additive) preprojective algebra as $R$-algebras if and…

We describe a method for an explicit determination of indecomposable preprojective and preinjective representations for extended Dynkin quivers by vector spaces and matrices. This method uses tilting theory and the explicit knowledge of…

The weighted triangulation algebras associated to triangulation quivers and their socle deformations were recently introduced and studied in [15]-[20] and [2]. These algebras, based on surface triangulations and originated from the theory…