Correction to Group algebras of finite representation type

Cluster-tilted Algebras of Finite Representation Type

We investigate the cluster-tilted algebras of finite representation type over an algebraically closed field. We give an explicit description of the relations for the quivers for finite representation type. As a consequence we show that a (basic) cluster-tilted algebra of finite type is uniquely determined by its quiver. Also some necessary conditions on the shapes of quivers of cluster-tilted a...

On Algebras of Finite Representation Type

Since D. G. Higman proved that bounded representation type and finite representation type are equivalent for group algebras at prime characteristic, there has been a renewed interest in the Brauer-Thrall conjecture that bounded representation type implies finite representation type for arbitrary algebras. The main purpose of this paper is to present a new approach to this conjecture by showing ...

Finite Generation Type Properties for Fuchsian Group Von Neumann Algebras

In this paper we prove the existence of finite systems G of generators, with special properties, for the von Neumann algebras L(Γ)⊗B(H), obtained by tensoring the group von Neumann algebra of a fuchsian group Γ with the bounded linear operators on a infinite dimensional, separable, Hilbert space H . The results show that the linear span of ordered monomials that are products of powers of adjoin...

A characterization of representation-finite algebras

Let A be a finite-dimensional, basic, connected algebra over an algebraically closed field. Denote by Γ (A) the Auslander–Reiten quiver of A. We show that A is representation-finite if and only if Γ (A) has at most finitely many vertices lying on oriented cycles and finitely many orbits with respect to the action of the Auslander–Reiten translation. Let K denote a fixed algebraically closed fie...

Representation theory of finite dimensional algebras