Maximal abelian subalgebras of complex orthogonal lie algebras

Abstract

The study of maximal abelian subalgebras (MASAs) of o(n,C) is reduced to the study of orthogonally indecomposable MASAs. Their classification is in turn reduced to that of maximal abelian nilpotent subalgebras (MANSs) of sl(n/2,C) (for n even) and of o(n,C) itself. General results and guidelines are given, making it possible to construct all MANSs, and hence all MASAs, for any given n. Representatives of all O(n,C) conjugacy classes of MASAs of o(n,C) are constructed for 2⩽n⩽7, as an application of the general techniques.