Semi-simple real subalgebras of non-compact semi-simple real Lie algebras. II

Abstract

The investigation of the problem of embedding a semi-simple real Lie algebra L ′ in a non-compact semi-simple real Lie algebra L that was begun in a previous paper is here extended to the case in which at least one of these real Lie algebras has A l as its complex extension and is obtained from the compact form SU( l+1) by an outer involutive automorphism. Detailed procedures are given for constructing all embeddings of L ′ in L when their corresponding complex Lie algebras are A l , B l or C l . These procedures are illustrated by considering examples corresponding to the complex Lie algebra embeddings A l −1⊂ A l , l⩾2, and C l ⊂ A 2 l −1, l⩾1, for which some new results are obtained.