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Mutation classes of skew-symmetrizable 3x3 matrices

Published 15 Dec 2010 in math.CO and math.RT | (1012.3318v2)

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.

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