Classification des triples de Manin pour les algèbres de Lie réductives complexes

Details Classification des triples de Manin pour les algèbres de Lie réductives complexes Classification des triples de Manin pour les algèbres de Lie réductives complexes

2000-03-21

arxiv.org/abs/math/0003123v1

Mathematics

Quantum Algebra

64 pages, LaTeX

Scientific paper

We study real and complex Manin triples for a complex reductive Lie algebra, $\g$. The first part includes, and extends to complex Manin triples, our earlier work [De]. First, we generalize results of E. Karolinsky, on the classification of Lagrangian subalgebras (cf.[K1], [K3]). Then we show that, if $\g$ is non commutative, one can attach, to each Manin triple in $\g$, another one for a strictly smaller reductive complex Lie subalgebra of $\g$. This gives a powerful tool for induction. Then we classify complex Manin triples, in terms of what we call generalized Belavin-Drinfeld data. In particular this generalizes, by other methods, the classification of A. Belavin and G. Drinfeld of certain $R$-matrices, i.e. the solutions of modified triangle equations for constants (cf [BD], Theorem 6.1). We get also results for real Manin triples. In passing, one retrieves a result of A. Panov [P1] which classifies certain Lie bialgebras structures on a real simple Lie algebra.

Affiliated with

Also associated with

No associations

Rating

Classification des triples de Manin pour les algèbres de Lie réductives complexes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Classification des triples de Manin pour les algèbres de Lie réductives complexes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Classification des triples de Manin pour les algèbres de Lie réductives complexes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-392612