This is the first of a two-volume set that provides a modern account of the representation
theory of finite dimensional associative algebras over an algebraically closed field. The …

In theory there is no difference between theory and practice. In practice there is. Yogi Berra
A SINGULAR Introduction to Commutative Algebra offers a rigorous intro duction to …

Mutation in triangulated categories and rigid Cohen–Macaulay modules Page 1 DOI:
10.1007/s00222-007-0096-4 Invent. math. 172, 117–168 (2008) Mutation in triangulated …

The cluster category associated with a finite-dimensional hereditary algebra was introduced
in [21](and in [26] for the An case). It serves in the representation-theoretic approach to …

We introduce the concept of maximal (n− 1)-orthogonal subcategories over Artin algebras
and orders, and develop (n+ 1)-dimensional Auslander–Reiten theory on them. We give the …

We investigate cluster-tilting objects (and subcategories) in triangulated 2-Calabi–Yau and
related categories. In particular, we construct a new class of such categories related to …

We study Auslander correspondence from the viewpoint of higher-dimensional analogue of
Auslander–Reiten theory [O. Iyama, Higher dimensional Auslander–Reiten theory on …

We study the category of matrix factorizations associated to the germ of an isolated
hypersurface singularity. This category is shown to admit a compact generator which is …

This is an introduction to some aspects of Fomin-Zelevinsky's cluster algebras and their links
with the representation theory of quivers and with Calabi-Yau triangulated categories. It is …

We study B-type D-branes in linear sigma models with Abelian gauge groups. The most
important finding is the grade restriction rule. It classifies representations of the gauge group …