Scalar products on Clifford modules and pseudo-\(H\)-type Lie algebras
The author introduces the notion of pseudo-Heisenberg type Lie algebras, that is, Lie algebras that are two-step nilpotent equipped with a scalar product of signature \((p,q)\), plus a compatibility condition with the Lie algebra structure. It is shown that a \((p,q)\)-algebra structure exists on a vector space if and only if a corresponding representation for the Clifford algebra \(\mathcal C(p,q)\) is admissible. So the existence of pseudo-\(H\)-type algebras is reduced to the existence of admissible modules. The author then proceeds to construct such modules for all pairs \((p,q)\). Finally he studies the admissibility of an irreducible \(\mathcal C(p,q)\)-module.
scientific article; zbMATH DE number 1985419
scientific article