This book is an introduction to the use of triangulated categories in the study of
representations of finite-dimensional algebras. In recent years representation theory has …

Modern developments in representation theory rely heavily on homological methods. This
book for advanced graduate students and researchers introduces these methods from their …

It is possible to associate a topological space to the category of modules over any ring. This
space, the Ziegler spectrum, is based on the indecomposable pure-injective modules …

Let Q be a quiver without oriented cycles and let α be a dimension vector such that Gl (α)
has an open orbit on the representation space R (α). We find representations {Si} and …

We investigate several homological aspects of recollements of abelian categories. In
particular, we study how various homological invariants and dimensions of the categories …

The class of support-tilting modules was introduced recently by Adachi et al. These modules
complete the class of tilting modules from the point of view of mutations. Given a finite …

In representation theory of finite-dimensional algebras,(semi) bricks are a generalization of
(semi) simple modules, and they have long been studied. The aim of this paper is to study …

In the work of Hoshino, Kato and Miyachi, 11, the authors look at t-structures induced by a
compact object, C, of a triangulated category, T, which is rigid in the sense of Iyama and …

A self-contained introduction is given to J. Rickard's Morita theory for derived module
categories and its recent applications in representation theory of finite groups. In particular …

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 …