Central extensions of the families of quasi-unitary Lie algebras

Abstract

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

References in corpus (2)

• Central Extensions of the Quasi-orthogonal Lie algebras
• The general solution of the real $Z_2^{\otimes N}$ graded contractions of $so(N+1)$

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• A perspective on the Magic Square and the 'special unitary' realizations of simple Lie algebras
• The family of quaternionic quasi-unitary Lie algebras and their central extensions