  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.
