On quasitilted algebras which are one-point extensions of hereditary algebras

On Bernstein Algebras Which Are Train Algebras

holds in A. This class of algebras was introduced by Holgate [4], following the original work of Bernstein [2] and subsequent investigations by Lyubich [5] on idempotent quadratic maps from a real simplex into itself. A summary of known results on Bernstein algebras (up to 1980) is given in Worz-Busekros [8], which will also be used as a basic reference on algebras in genetics. All definitions ...

Skew group algebras of piecewise hereditary algebras are piecewise hereditary

The aim of this paper is twofold. First, we show that the main results of HappelRickard-Schofield (1988) and Happel-Reiten-Smalø (1996) on piecewise hereditary algebras are coherent with the notion of group action on an algebra. Then, we take advantage of this compatibility and show that if G is a finite group acting on a piecewise hereditary algebra A over an algebraically closed field whose c...

Tilting Theory and Quasitilted Algebras

On Coalgebras which are Algebras

The category CoalgΣ of coalgebras with respect to a (bounded) signature Σ is known to be locally finitely presentable (see [1]). We strenghten this result by showing that CoalgΣ even is a presheaf category. Moreover, we give a presentation of this category as the category of all algebras of some (many-sorted) signature (without any equations). Σ–coalgebras, i.e., coalgebras with respect to a po...

On Auslander–Reiten components for quasitilted algebras

An artin algebra A over a commutative artin ring R is called quasitilted if gl.dimA ≤ 2 and for each indecomposable finitely generated A-module M we have pdM ≤ 1 or idM ≤ 1. In [11] several characterizations of quasitilted algebras were proven. We investigate the structure and homological properties of connected components in the Auslander–Reiten quiver ΓA of a quasitilted algebra A. Let A be a...