Related papers: Tame hereditary path algebras and amenability

We prove that there are no strictly shod algebras in hereditary gentle algebras by geometric models. As an application, we give a classification of the silted algebras for Dynkin type $\mathbb{A}_{n}$ and $\widetilde{\mathbb{A}}_{n}$.

In this paper we find some necessary and sufficient conditions for a Banach algebra to be amenable or weakly amenable, by applying the homomorphisms on Banach algebras.

For a fixed finite dimensional algebra $A$, we study representation embeddings of the form $mod(B)\rightarrow mod(A)$. Such an embedding is called homological, if it induces an isomorphism on all Ext-groups and weakly homological, if only…

We explore the (noncommutative) geometry of locally simple representations of the diagonal locally finite Lie algebras $\mathfrak{sl}(n^\infty)$, $\mathfrak o(n^\infty)$, and $\mathfrak{sp}(n^\infty)$. Let $\mathfrak g_\infty$ be one of…

In this article, gentle algebras are realised as tiling algebras, which are associated to partial triangulations of unpunctured surfaces with marked points on the boundary. This notion of tiling algebras generalise the notion of Jacobian…

We consider the tensor product of modules over the polynomial algebra corresponding to the usual tensor product of linear operators. We present a general description of the representation ring in case the ground field k is perfect. It is…

We show that for a Banach algebra $A$ with a bounded approximate identity, the amenability of the projective tensor product of A with A, the amenability of the projective tensor product of A with A^{op}and the amenability of A are…

We prove that every finite dimensional algebra over an algebraically closed field is either derived tame or derived wild. We also prove that any deformation of a derived tame algebra is derived tame.

A GR-segment for an artin algebra is a sequence of Gabriel-Roiter measures, which is closed under direct predecessors and successors. The number of the GR-segments indexed by natural numbers $\mathbb{N}$ and integers $\mathbb{Z}$ probably…

In this paper we study a certain class of central extensions of preprojective algebras of quivers under the name quiver Heisenberg algebras (QHA). There are several classes of algebras introduced before by different researchers from…

Let $\mathfrak{g}$ be an affine Kac-Moody algebra with symmetric Cartan datum, $\mathfrak{n^{+}}$ be the maximal nilpotent subalgebra of $\mathfrak{g}$. By the Hall algebra approach, we construct integral bases of the $\mathbb{Z}$-form of…

A quasi-hereditary algebra is an Artin algebra together with a partial order on its set of isomorphism classes of simple modules which satisfies certain conditions. In this article we investigate all the possible choices that yield to…

We call a finite-dimensional K-algebra A geometrically irreducible if for all d, all connected components of the affine scheme of d-dimensional A-modules are irreducible. We show that the geometrically irreducible algebras without loops…

We show that the representation type of the Jacobian algebra P(Q,S) associated to a 2-acyclic quiver Q with non-degenerate potential S is invariant under QP-mutations. We prove that, apart from very few exceptions, P(Q,S) is of tame…

We use folding techniques to define a new class of gentle-like algebras that generalise the iterated tilted algebras of type $C$ and $\widetilde{C}$, which we call folded gentle algebras. We then show that folded gentle algebras satisfy…

We introduce the notion of amenability for affine algebras. We characterize amenability by Folner-sequences, paradoxicality and the existence of finitely invariant dimension-measures. Then we extend the results of Rowen on ranks, from…

This paper generalizes former works of Derksen, Weyman and Zelevinsky about quivers with potentials. We consider semisimple finite-dimensional algebras $E$ over a field $F$, such that $E \otimes_{F} E^{op}$ is semisimple. We assume that $E$…

It is shown that, given any finite dimensional, split basic algebra $\Lambda = K\Gamma/I$ (where $\Gamma$ is a quiver and $I$ an admissible ideal in the path algebra $K \Gamma$), there is a finite list of affine algebraic varieties, the…

Let $A$ be a finitary algebra over a finite field $k$, and $A$-$mod$ the category of finite dimensional left $A$-modules. Let $\mathcal{H}(A)$ be the corresponding Hall algebra, and for a positive integer $r$ let $D_{r}(A)$ be the subspace…

Let k be an algebraically closed field. Given an extension A : B of finite-dimensional k- algebras, we establish criteria ensuring that the representation-theoretic notion of polynomial growth is preserved under ascent and descent. These…