On the classifications of unitary matrices

Abstract

We classify the dynamical action of matrices in SU(p,q) using the coefficients of their characteristic polynomial. This generalises earlier work of Goldman for SU(2,1) and the classical result for SU(1,1), which is conjugate to SL(2,ℝ). As geometrical applications, we show how this enables us to classify automorphisms of real and complex hyperbolic space and anti de Sitter space.