Maximal green sequences of skew-symmetrizable 3 x 3 matrices

2014-01-01
Maximal green sequences are particular sequences of mutations of skew-symmetrizable matrices which were introduced by Keller in the context of quantum dilogarithm identities and independently by Cecotti-Cordova-Vafa in the context of supersymmetric gauge theory. In this paper we study maximal green sequences of skew-symmetrizable 3 x 3 matrices. We show that such a matrix with a mutation-cyclic diagram does not have any maximal green sequence. We also obtain some basic properties of maximal green sequences of skew-symmetrizable matrices with mutation-acyclic diagrams.

Citation Formats
A. İ. Seven, “Maximal green sequences of skew-symmetrizable 3 x 3 matrices,” LINEAR ALGEBRA AND ITS APPLICATIONS, vol. 440, pp. 125–130, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/47040.