Classification des triples de Manin pour les algèbres de Lie réductives complexes: Avec un appendice de Guillaume Macey
✍ Scribed by Patrick Delorme
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 533 KB
- Volume
- 246
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
We study real and complex Manin triples for a complex reductive Lie algebra ᒄ.
Ž First, we generalize results of E. Karolinsky 1996, Math. Phys. Anal. Geom 3, . 545᎐563; 1999, Preprint math.QA.9901073 on the classification of Lagrangian subalgebras. Then we show that, if ᒄ is noncommutative, one can attach to each Manin triple in ᒄ another one for a strictly smaller reductive complex Lie subalgebra of ᒄ. This gives a powerful tool for induction. Then we classify complex Manin triples in terms of what we call generalized Belavin᎐Drinfeld data. This generalizes, by other methods, the classification of A. Belavin and V. G. Drinfeld of certain r-matrices, i.e., the solutions of modified triangle equations for constants