Mutation classes of skew-symmetrizable 3x3 matrices

Abstract

In this paper, we determine representatives for the mutation classes of skew-symmetrizable 3x3 matrices and associated graphs using a natural minimality condition, generalizing and strengthening results of Beineke-Brustle-Hille and Felikson-Shapiro-Tumarkin. Furthermore, we obtain a new numerical invariant for the mutation operation on skew-symmetrizable matrices of arbitrary size.

arXiv comment12 pages, minor corrections; final version to appear in Proc.Amer.Math.Soc

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