A CLASS OF HOMOGENEOUS SEMISIMPLE SPACES

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A CLASS OF HOMOGENEOUS SEMISIMPLE SPACES

The semisimple structure, which generalizes the complex and the paracomplex structures, is considered. The authors classify all the homogeneous semisimple spaces whose underlying spaces are $G/C(W)_{0}$, where $G$ is a real simple Lie Group, $W\in \frak g$,$C(W)_0$ is the identity component of the centralizer $C(W)$ of $W$ in $G$.