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
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10.1512/iumj.2007.56.2932
10.1512/iumj.2007.56.2932
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Indiana Univ. Math. J. 56 (2007) 1233 - 1260
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