IUMJ

Title: Homogeneous spaces with invariant flat Cartan structures.

Authors: A. Martin Mendez and J.F. Torres Lopera

Issue: Volume 56 (2007), Issue 3, 1233-1260

Abstract:

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.