Related papers: Preprojective algebras of tree-type quivers

In arXiv:1104.4441 it was shown that any 1-quasi-hereditary algebra affords a particular basis which is related to a given partial order on the set of simple modules. We show that the modules generated by these basis-elements are also…

Rooted tree maps assign to an element of the Connes-Kreimer Hopf algebra of rooted trees a linear map on the noncommutative polynomial algebra in two letters. Evaluated at any admissible word these maps induce linear relations between…

In this paper we show that acyclic $n$-slice algebras are exactly acyclic $n$-hereditary algebras whose $(n+1)$-preprojective algebras are $(q+1,n+1)$-Koszul. We also list the equivalent triangulated categories arising from the algebra…

Let Q be a strongly locally finite quiver and denote by rep(Q) the category of locally finite dimensional representations of Q over some fixed field k. The main purpose of this paper is to get a better understanding of rep(Q) by means of…

We study quivers with relations given by non-commutative analogs of Jacobian ideals in the complete path algebra. This framework allows us to give a representation-theoretic interpretation of quiver mutations at arbitrary vertices. This…

We provide a categorification of Oh and Suh's combinatorial Auslander-Reiten quivers in the simply laced case. We work within the perfectly valued derived category $\mathrm{pvd}(\Pi_Q)$ of the 2-dimensional Ginzburg dg algebra of a Dynkin…

Let $A$ be an algebra over a field $K$ of characteristic zero, let $\d_1, >..., \d_s\in \Der_K(A)$ be {\em commuting locally nilpotent} $K$-derivations such that $\d_i(x_j)=\d_{ij}$, the Kronecker delta, for some elements $x_1,..., x_s\in…

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 preprojective algebra of a finite EI quiver. We prove that it is isomorphic to a centain tensor algebra. For a finite EI quiver of Cartan type, we prove that the corresponding preprojective algebra is isomorphic to the…

We introduce the notion of the moduli stack of relations of a quiver. When the quiver with relations is derived-equivalent to an algebraic variety, the corresponding compact moduli scheme can be viewed as a compact moduli of noncommutative…

Let $K$ denote an algebraically closed field with characteristic 0, and let $q$ denote a nonzero scalar in $K$ that is not a root of unity. Let $A_q$ denote the unital associative $K$-algebra defined by generators $x,y$ and relations…

We introduce some basic concepts for Jacobi-Jordan algebras such as: representations, crossed products or Frobenius/metabelian/co-flag objects. A new family of solutions for the quantum Yang-Baxter equation is constructed arising from any…

A commutative diagram that connects the basic objects of commutative algebra with the main objects of commutative analysis is constructed. Namely, with the help of five types of canonical embeddings we constructed a diagram between two sets…

Any finite dimensional semisimple algebra A over a field K is isomorphic to a direct sum of finite dimensional full matrix rings over suitable division rings. In this paper we will consider the special case where all division rings are…

Let $K$ be an infinite field and $K< X> =K< X_1,...,X_n>$ the free associative algebra generated by $X=\{X_1,...,X_n\}$ over $K$. It is proved that if $I$ is a two-sided ideal of $K< X>$ such that the $K$-algebra $A=K< X> /I$ is almost…

We consider graded twisted Calabi-Yau algebras of dimension 3 which are derivation-quotient algebras of the form $A = \kk Q/I$, where $Q$ is a quiver and $I$ is an ideal of relations coming from taking partial derivatives of a twisted…

We describe a presentation for the descent algebra of the symmetric group $\sym{n}$ as a quiver with relations. This presentation arises from a new construction of the descent algebra as a homomorphic image of an algebra of forests of…

Let $Q$ be a finite quiver without oriented cycles and $k$ an algebraically closed field.In this paper we establish a connection between cluster algebras and the representation theory of the path algebra $kQ$, in terms of the spectral…

Any cluster-tilted algebra is the relation extension of a tilted algebra. We present a method to, given the distribution of a cluster-tilting object in the Auslander-Reiten quiver of the cluster category, construct all tilted algebras whose…

We consider $\Lambda$ an artin algebra and $n \geq 2$. We study how to compute the left and right degrees of irreducible morphisms between complexes in a generalized standard Auslander-Reiten component of ${\mathbf{C_n}({\rm proj}\,…