Congruence invariants of matrix mutation

Abstract

Motivated by the recent work of R. Casals on binary invariants for matrix mutation, we study the matrix congruence relation on quasi-Cartan matrices. We obtain a classification and determine normal forms modulo 4. We also establish their mutation invariance properties. In particular, we obtain new mutation invariants, which include the one obtained by R. Casals.

14 pages; minor editorial changes