Central extensions of the families of quasi-unitary Lie algebras

Herranz, F. J.; Bueno, J. C. Pérez; Santander, M.

Central extensions of the families of quasi-unitary Lie algebras

Authors

Herranz, F. J.

Bueno, J. C. Pérez

Santander, M.

Description

The most general possible central extensions of two whole families of Lie algebras, which can be obtained by contracting the special pseudo-unitary algebras su(p,q) of the Cartan series A_l and the pseudo-unitary algebras u(p,q), are completely determined and classified for arbitrary p,q. In addition to the su(p,q) and u({p,q}) algebras, whose second cohomology group is well known to be trivial, each family includes many non-semisimple algebras; their central extensions, which are explicitly given, can be classified into three types as far as their properties under contraction are involved. A closed expression for the dimension of the second cohomology group of any member of these families of algebras is given.
23 pages. Latex2e file