The present notes are a more or" less faithful reproduction of lectures given at the Workshop
on the present trends in Representation Theory, Carleton University, Ottawa, 19F9. Some …

The aim of this paper is to introduce τ-tilting theory, which 'completes'(classical) tilting theory
from the viewpoint of mutation. It is well known in tilting theory that an almost complete tilting …

This textbook is an introduction to the representation theory of finite-dimensional algebras
with a strong emphasis on quivers and their representations. The book is intended to be …

We introduce a new class of algebras, which we call cluster-tilted. They are by definition the
endomorphism algebras of tilting objects in a cluster category. We show that their …

The aim of this paper is to provide direct proofs for the main results on tilted algebras
obtained by Happel-Ringel in [9 J• It seems to us that the search for direct proofs is justified …

We study a triangulated category of graded matrix factorizations for a polynomial of type
ADE. We show that it is equivalent to the derived category of finitely generated modules over …

A recurring theme in a traditional introductory graduate algebra course is the existence and
consequences of relationships between different algebraic structures. This is also the theme …

Apart from confirming conjectures in algebraic combinatorics and integrable systems, having
an interesting representation theory, and connecting with real algebraic geometry …

Throuzhout this article k denotes an alzebraically closed field, A a finite-dimensional
associative k-algebra with unit element IA= I and mod A the care@ cry of unitary right A …

Let R be a finite dimensional hereditary algebra. We are concerned with the problem of
determining the indecomposable R-modules of finite length. This problem completely has …