Complex product structures on some simple Lie groups

Details Complex product structures on some simple Lie groups Complex product structures on some simple Lie groups

2004-05-31

arxiv.org/abs/math/0405584v2

Mathematics

Differential Geometry

latex, 7 pages

Scientific paper

We construct invariant complex product (hyperparacomplex, indefinite quaternion) structures on the manifolds underlying the real noncompact simple Lie groups $SL(2m-1,\RR)$, $SU(m,m-1)$ and $SL(2m-1,\CC)^\RR$. 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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