Related papers: Piecewise hereditary algebras under field extensio…

Let G be an algebraic group defined over an algebraically closed field k of characteristic zero. We give a simple proof of the following result: if H^1(L, G) = {1} for some finitely generated field extension L/k of transcendence degree \ge…

A basic finite dimensional algebra over an algebraically closed field $k$ is isomorphic to a quotient of a tensor algebra by an admissible ideal. The category of left modules over the algebra is isomorphic to the category of representations…

Happel and Seidel gave a classification of piecewise hereditary Nakayama algebras, where the relations are given by some power of the radical. Here we explore what happens for general relations. We develop techniques for showing that a…

Let $A$ be a finite dimensional algebra over an algebraically closed field $\mathbf{k}$. If $A$ is quasi-hereditary and the projective dimensions of all standard modules are at most one, then $A$ is called left strongly quasi-hereditary. In…

We use a generalization of a construction by Ziegler to show that for any field $F$ and any countable collection of countable subsets $A_i \subseteq F, i \in \calI \subset \Z_{>0}$ there exist infinitely many fields $K$ of arbitrary…

Establishing whether an algebra is quasi-hereditary or not is, in general, a difficult problem. In this paper we introduce a sufficient criterion to determine whether a general finite dimensional algebra is quasi-hereditary by showing that…

Let $K$ be a complete discretely valued field of rank one, with residue field $\Q_p$. It is well known that period equals index in $\Br(K)$. We prove that when $p=2$ there exist noncyclic $K$-division algebras of every $2$-power degree…

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…

A category is called {\em split} if for every morphism $s\colon X\to Y$ there exists a morphism $t\colon Y\to X$ such that $s\circ t\circ s = s$. Let $C$ be a finite split category, let $k$ be a field of characteristic 0 and let $\alpha$ be…

Let $k$ be a field and suppose $p, q\in k$. We prove that the two affine Hecke algebras $H_q$ and $H_p$ of type $A_n$ are isomorphic as $k$-algebras if and only if $p=q^{\pm 1}$.

We show that if H is a hereditary finite dimensional algebra, M is a finitely generated H-module and B is a semisimple subalgebra of the endomorphism algebra of M, then the representation dimension of the corresponding triangular matrix…

We give bounds on the global dimension of a finite length, piecewise hereditary category in terms of quantitative connectivity properties of its graph of indecomposables. We use this to show that the global dimension of a finite…

We develop the theory of ``branch algebras'', which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting…

We present a study on the description of incidence algebras that are piecewise hereditary, which we denominate Phia algebras. We describe the quiver with relations of the Phia algebras of Dynkin type and introduce a new family of Phia…

We determine the structure of all finite-dimensional self-injective algebras over a field whose Auslander-Reiten quiver admits a hereditary stable slice.

Let k be a field, let A a finite-dimensional hereditary k-algebra. We consider the category of all finite-dimensional A-modules. We are going to characterize the representation type of A (tame or wild) in terms of the possible subcategories…

We deal with the existing problem of filtered multiplicative bases of finite-dimensional associative algebras. For an associative algebra A over a field, we investigate when the property of having a filtered multiplicative basis is…

We examine situations, where representations of a finite-dimensional $F$-algebra $A$ defined over a separable extension field $K/F$, have a unique minimal field of definition. Here the base field $F$ is assumed to be a $C_1$-field. In…

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…

We describe necessary and sufficient conditions for the hereditarity of the category algebra of an infinite EI category satisfying certain combinatorial assumptions. More generally, we discuss conditions such that the left global dimension…