## arXiv Analytics

### arXiv:physics/9801008 [math-ph]AbstractReferencesReviewsResources

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

Published 1998-01-08Version 1

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.

$\mathbb{Z}_2 \times \mathbb{Z}_2$ generalizations of infinite dimensional Lie superalgebra of conformal type with complete classification of central extensions