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 …

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 …

The concept of cluster tilting gives a higher analogue of classical Auslander correspondence
between representation-finite algebras and Auslander algebras. The n-Auslander–Reiten …

Let Q be a finite quiver without oriented cycles, let Λ be the associated preprojective algebra,
let g be the associated Kac–Moody Lie algebra with Weyl group W, and let n be the positive …

A general framework for cluster tilting is set up by showing that any quotient of a triangulated
category modulo a tilting subcategory (ie, a maximal 1-orthogonal subcategory) carries an …

We say that an algebra $\Lambda $ over a commutative noetherian ring $ R $ is Calabi-Yau
of dimension $ d $($ d $-CY) if the shift functor $[d] $ gives a Serre functor on the bounded …

Abstract We introduce (n+ 1)-preprojective algebras of algebras of global dimension n. We
show that if an algebra is n-representation-finite then its (n+ 1)-preprojective algebra is self …

Cluster categories were introduced in 2006 by Buan-Marsh-Reineke-Reiten-Todorov in
order to categorify acyclic cluster algebras without coefficients. Their construction was …

We introduce the notion of $ n $-representation-finiteness, generalizing representation-finite
hereditary algebras. We establish the procedure of $ n $-APR tilting and show that it …