Cluster-tilted algebras

2006322 citationsJournal Articlebronze Open Access

Authors

Aslak Bakke Buan · Norwegian University of Science and Technology

Idun Reiten · Norwegian University of Science and Technology

Abstract

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 representation theory is very close to the representation theory of hereditary algebras. As an application of this, we prove a generalised version of so-called APR-tilting.

Topics & Keywords

Algebraic structures and combinatorial models Advanced Topics in Algebra Nonlinear Waves and Solitons

UN Sustainable Development Goals

Reduced inequalities

Publication Details

Published in: Transactions of the American Mathematical Society

Volume 359, Issue 1, pp. 323-332

DOI: 10.1090/s0002-9947-06-03879-7

Field-Weighted Citation Impact: 28.48