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

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

2008-03-27

arxiv.org/abs/0803.3907v2

J. Pure Appl. Algebra 213 (2009) pp. 1438-1449

Mathematics

Representation Theory

15 pages, a mistake in the references has been corrected

Scientific paper

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.

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