Classification des triples de Manin pour les algèbres de Lie réductives complexes
| dc.creator | Delorme, Patrick | |
| dc.date | 2000-03-21 | |
| dc.date.accessioned | 2026-07-07T04:34:22Z | |
| dc.date.available | 2026-07-07T04:34:22Z | |
| dc.description | 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. | |
| dc.description | 64 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0003123 | |
| dc.identifier | http://arxiv.org/abs/math/0003123 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58877 | |
| dc.subject | Quantum Algebra | |
| dc.title | Classification des triples de Manin pour les algèbres de Lie réductives complexes | |
| dc.type | text |