Homological invariants of generalized bound path algebras

We study some homological invariants of a given generalized bound path algebra in terms of those of the algebras used in its construction. As a consequence, we are also able to construct generalized bound path algebras which are shod or quasitilted

On the composite of three irreducible morphisms over string algebras

We characterize the representation- nite triangular string algebras having a path of irreducible morphisms of length three between pairwise non-isomorphic modules whose composite lies in the fourth power of the radical

Basic representation theory of algebras

This textbook introduces the representation theory of algebras by focusing on two of its most important aspects: the Auslander-Reiten theory and the study of the radical of a module category. It starts by introducing and describing several characterisations of the radical of a module category, then presents the central concepts of irreducible morphisms and almost split sequences, before providing the definition of the Auslander-Reiten quiver, which encodes much of the information on the module category. It then turns to the study of endomorphism algebras, leading on one hand to the definition of the Auslander algebra and on the other to tilting theory. The book ends with selected properties of representation-finite algebras, which are now the best understood class of algebras. Intended for graduate students in representation theory, this book is also of interest to any mathematician wanting to learn the fundamentals of this rapidly growing field. A graduate course in non-commutative or homological algebra, which is standard in most universities, is a prerequisite for readers of this book