相关论文: Tame (hereditary) algebras of amenable representat…

We classify the representation type of the descent algebras of type $\A$ in the positive characteristic case. The algebras have finite representation type only for a few small degrees; otherwise, they are wild. Our main reduction method…

We show that $\tau$-tilting finite simply connected algebras are representation-finite. Then, some related algebras are considered, including iterated tilted algebras, tubular algebras and so on. We also prove that the $\tau$-tilting…

We consider affine representable algebras, that is, finitely generated algebras over a field that can be embedded into some matrix algebra over a commutative algebra. We show that this algebra can in fact be chosen to be a polynomial…

Let E be an arbitrary directed graph with no restrictions on the number of vertices and edges and let K be any field. We give necessary and sufficient conditions for the Leavitt path algebra L_K(E) to be of countable irreducible…

A complete classification and character formulas for finite-dimensional irreducible representations of the rational Cherednik algebra of type A is given. Less complete results for other types are obtained. Links to the geometry of affine…

Associative algebras with involution over a field of zero characteristic are considered. It is proved that in this case for any finitely generated associative algebra with involution there exists a finite dimensional algebra with involution…

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.

Let k be an algebraically closed field of characteristic p> 0. For a basic classical Lie superalgebra, we show its restricted cohomology algebra is a finitely generated algebra. Thus the cohomological support theory can be established. As a…

We give the first examples of (non-amenable group) amenable actions on stably finite simple C*-algebras. More precisely, we give such actions for any countable group in an explicit way. The main ingredients of our construction are the full…

We consider quiver representations respecting a quiver automorphism and show that the dimension vectors of the indecomposables are precisely the positive roots of an associated symmetrisable Kac-Moody Lie algebra. Moreover, every such Lie…

In this paper we show that evolution algebras over any given field $\Bbbk$ are universally finite. In other words, given any finite group $G$, there exist infinitely many regular evolution algebras $X$ such that $Aut(X)\cong G$. The proof…

Let $A$ be a tame hereditary algebra over a finite field $k$ with $q$ elements, and ${\bar{A}}$ be the duplicated algebra of $A$. In this paper, we investigate the structure of Ringel-Hall algebra $\mathscr{H} (\bar{A})$ and of the…

The Lie algebra of planar vector fields with coefficients from the field of rational functions over an algebraically closed field of characteristic zero is considered. We find all finite-dimensional Lie algebras that can be realized as…

In this paper, we classify all Leavitt path algebras which have the property that every Lie ideal is an ideal. As an application, we show that Leavitt path algebras with this property provide a class of locally finite, infinite-dimensional…

We study the representation theory of finite-dimensional $\omega$-Lie algebras over the complex field. We derive an $\omega$-Lie version of the classical Lie's theorem, i.e., any finite-dimensional irreducible module of a soluble…

Let $p$ be a prime number, and let $k$ be an algebraically closed field of characteristic $p$. We show that the tame fundamental group of a smooth affine curve over $k$ is a projective profinite group. We prove that the fundamental group of…

In this paper, we give new proofs of the celebrated Andr\'eka-Resek-Thompson representability results of certain axiomatized cylindric-like algebras. Such representability results provide completeness theorems for variants of first order…

Let $k$ be an algebraically closed field and let $A$ be a finitely generated $k-$algebra. We show that the scheme of n-dimensional representations of $A$ is smooth when $A$ is hereditary and coherent. We deduce from this the smoothness of…

Let $A$ be a finite dimensional hereditary algebra over an algebraically closed field and $A^{(m)}$ the $m$-replicated algebra of $A$. We prove that the representation dimension of $A^{(m)}$ is at most three, and that the dominant dimension…

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…