The families of orthogonal, unitary and quaternionic unitary Cayley--Klein algebras and their central extensions

Details The families of orthogonal, unitary and quaternionic unitary Cayley--Klein algebras and their central extensions The families of orthogonal, unitary and quaternionic unitary Cayley--Klein algebras and their central extensions

1999-07-26

arxiv.org/abs/math-ph/9907021v1

Physics

Mathematical Physics

10 pages, LaTeX. Contribution to the III Classical and Quantum Integrable Systems. Edited by L.G. Mardoyan, G.S. Pogosyan and

Scientific paper

The families of quasi-simple or Cayley--Klein algebras associated to antihermitian matrices over R, C and H are described in a unified framework. These three families include simple and non-simple real Lie algebras which can be obtained by contracting the pseudo-orthogonal algebras so(p,q) of the Cartan series $B_l$ and $D_l$, the special pseudo-unitary algebras su(p,q) in the series $A_l$, and the quaternionic pseudo-unitary algebras sq(p,q) in the series $C_l$. This approach allows to study many properties for all these Lie algebras simultaneously. In particular their non-trivial central extensions are completely determined in arbitrary dimension.

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