Central extensions of the families of quasi-unitary Lie algebras

The most general possible central extensions of two whole families of Lie algebras, which can be obtained by contracting the special pseudo-unitary algebras of the Cartan series and the pseudo-unitary algebras , are completely determined and classified for arbitrary p and q. In addition to the and 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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