Sur les triples de Manin pour les algèbres de Lie réductives complexes

Details Sur les triples de Manin pour les algèbres de Lie réductives complexes Sur les triples de Manin pour les algèbres de Lie réductives complexes

1999-12-07

arxiv.org/abs/math/9912055v2

Mathematics

Quantum Algebra

43 pages, LaTeX, minor corrections

Scientific paper

We study Manin triples for a reductive Lie algebra, $\g$. First, we generalize results of E. Karolinsky, on the classification of Lagrangian subalgebras (cf. KAROLINSKY E., {\em A Classification of Poisson homogeneous spaces of a compact Poisson Lie group}, Dokl. Ak. Nauk, 359 (1998), 13-15). Then we show that, if $\g$ is non commutative, one can attach, to each Manin triple in $\g$, an other one for a strictly smaller reductive complex Lie subalgebra of $\g$. We study also the inverse process.

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