A class of homogeneous semisimple spaces (Q1266287)

A semisimple structure on a smooth manifold \(M\) is defined by a tensor field \(I\) of type \((1,1)\) such that 1. there exists a real polynomial \(f(x)\) without multiple roots such that \(f(I)=0\); 2. the Nijenhuis tensor \(N(X,Y)= I^2[X,Y]- I[IX,Y]- I[X,IY]+ [IX,IY]=0\). It is a natural generalization of the complex and para-complex structures. The homogeneous semisimple structure is defined in a natural manner. The authors classify homogeneous spaces \(M=G/C(W)_0\) where \(G\) is a real or complex connected semisimple Lie group, \(C(W)\) the centralizer of a semisimple element \(W\) of the Lie algebra \(g\) of \(G\), \(C(W)_0\) the identity component of \(C(W)\).