Generalized conformal pseudo-Galilean algebras and their Casimir operators

A generalization Gal(l) (p, q) of the conformal Galilei algebra g(l) (d) with Levi subalgebra isomorphic to sl(2, R) circle plus so(p, q) is introduced and a virtual copy of the latter in the enveloping algebra of the extension is constructed. Explicit expressions for the Casimir operators are obtained from the determinant of polynomial matrices. For the central factor algebra (Gal) over bar (l) (p, q), an exact formula giving the number of invariants is obtained and a procedure to compute invariant functions that do not depend on the variables of the Levi subalgebra is developed. It is further shown that such solutions determine complete sets of invariants provided that the relation d <= 2l + 2 is satisfied.