Homogeneous spaces with invariant flat Cartan structures. J.F. LoperaA. Mendez 53C1053C15homogeneous spacesstructures of graded type Let $L/L'$ be a homogeneous space associated with a semi-simple graded Lie algebra $\mathfrak{l} = \mathfrak{l}_{-1} \oplus \mathfrak{l}_0 \oplus \mathfrak{l}_{1}$. On a homogeneous space $G/H$, with $H$ connected, the existence of a $G$-invariant flat Cartan structure of graded type $L/L'$ is equivalent to the existence of a homomorphism $f \colon \mathfrak{g} \to \mathfrak{l}$ of the Lie algebra $\mathfrak{g}$ of $G$ into $\mathfrak{l}$ satisfying natural conditions. Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.2932 10.1512/iumj.2007.56.2932 en Indiana Univ. Math. J. 56 (2007) 1233 - 1260 state-of-the-art mathematics http://iumj.org/access/