Grothendieck Group and Generalized Mutation Rule for 2-Calabi--Yau Triangulated Categories

Abstract

We compute the Grothendieck group of certain 2-Calabi--Yau triangulated categories appearing naturally in the study of the link between quiver representations and Fomin--Zelevinsky's cluster algebras. In this setup, we also prove a generalization of Fomin--Zelevinsky's mutation rule.

arXiv comment15 pages, a mistake in the references has been corrected