Maximal Abelian subalgebras of pseudounitary lie algebras

AbstractThe task of classifying and constructing all maximal Abelian subalgebras of su(p,q) (p⩾q⩾1) is reduced to that of classifying orthogonally indecomposable MASAs. These are either maximal Abelian nilpotent subalgebras (represented by nilpotent matrices in any finite-dimensional representation), or for p=q they can be (nonorthogonally) decomposable and their study can be reduced to a construction of MANSs of sl(p,C). Two types of MANSs of su(p,q) are shown to exist (“one-rowed” and “non-one-rowed”). Numerous classification theorems are proven and applied to obtain all MASAs of su(p,1), su(p,2), and su(p,q) with p+q⩽6. Physical applications are discussed