Central extensions of the families of quasi-unitary Lie algebras

Details Central extensions of the families of quasi-unitary Lie algebras Central extensions of the families of quasi-unitary Lie algebras

1998-01-08

arxiv.org/abs/physics/9801008v1

J.Phys.A31:5327-5347,1998

Physics

Mathematical Physics

23 pages. Latex2e file

Scientific paper

10.1088/0305-4470/31/23/015

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.

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