Maximal Abelian subalgebras of complex Euclidean Lie algebras

Abstract

Maximal Abelian subalgebras (MASAs) of the complex Euclidean Lie algebra [Formula: see text] are classified into conjugacy classes under the action of the Lie group [Formula: see text] Use is made of an earlier classification of MASAs of the orthogonal Lie algebra [Formula: see text] These are then extended to nonsplitting MASAs of [Formula: see text] in which maximal Abelian nilpotent subalgebras of [Formula: see text] are coupled with translations in a nontrivial manner. The methods presented are applicable to the classification of MASAs of any affine Lie algebra.