Some Observations on Enveloping Algebras of Noncompact Groups

In order to provide the particle physicist with useful mathematical tools (and a large number of interesting identities), the enveloping algebras of the noncompact homogeneous O(p, q), U(p, q), and inhomogeneous IO(p, q), IU(p, q) groups are discussed in some detail. The construction of the generators of O(p, q + 1) and O(p + 1, q) from the enveloping algebra of IO(p, q) and the analog result for the corresponding pseudo-unitary groups are also presented.