Complexifications of Symmetric Spaces. I.
Generalizing Hermitian and pseudo-Hermitian spaces,
we define twisted complex symmetric spaces, and we show that
they correspond to an algebraic object called Hermitian Jordan
triple product. The main topic of this work is to investigate the
class of real forms of twisted complex symmetric spaces,
called the category of symmetric spaces with twist. We show that
this category is equivalent to the category of all real Jordan triple systems,
and we can use work of B.O. Makarevic in order
to classify the irreducible spaces. The classification shows that most
irreducible symmetric spaces have exactly one twisted complexification.
This leads to open problems concerning the relation of Jordan and
Lie triple systems.
(This paper has appeared in Trans. AMS. 353 (2001), pp. 2531 -- 2556)
W. Bertram
<Wolfgang.Bertram@antares.iecn.u-nancy.fr>