Complex product structures on some simple Lie groups
Abstract
We construct invariant complex product (hyperparacomplex, indefinite quaternion) structures on the manifolds underlying the real noncompact simple Lie groups SL(2m-1,), SU(m,m-1) and SL(2m-1,). We show that on the last two series of groups some of these structures are compatible with the biinvariant Killing metric. Thus we also provide a class of examples of compact (neutral) hyperparahermitean, non-flat Einstein manifolds.
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