Normal forms of elements of classical real and complex Lie and Jordan algebras

Abstract

Elements of the classical complex and real Lie and Jordan algebras with involutions are classified into conjugacy classes under the action of the corresponding classical Lie group. Normal forms of representatives of each conjugacy class are chosen so as to resemble the Jordan normal forms of n×n complex matrices. For completeness similar results are given for gl(n,C), gl(n,R), and gl(n,H).