Timeline for Which Lie algebra admit symplectic forms
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Aug 3, 2011 at 8:11 | comment | added | amine | Thanks, Nicola! Now, it's an elementary fact that a solution $r$ of the classical Yang-Baxter equation defines a Lie algebra homomorphism $r_\sharp : \mathcal{G}^*\rightarrow\mathcal{G}$ such that $$\omega(x,y)=r_\sharp(\alpha,\beta)$$ (where $r_\sharp(\alpha)=x$, $r_\sharp(\beta)=y$) is a well defined symplectic form on $\mathrm{Im}r$. | |
| Aug 1, 2011 at 18:11 | comment | added | Nicola Ciccoli | Thanks Jose, i was out with the iPad and couldn't provide details... | |
| Aug 1, 2011 at 16:56 | comment | added | José Figueroa-O'Farrill | Sorry, that's D.V. Alekseevsky! | |
| Aug 1, 2011 at 16:55 | comment | added | José Figueroa-O'Farrill | The citation is D.K Alekseevsky A.M. Perelomov, Journal of Geometry and Physics 22 (1997) 191-211. The MathSciNet entry is ams.org/mathscinet-getitem?mr=1453001 which has links to the article (behind an Elsevier paywall). | |
| Aug 1, 2011 at 16:41 | history | answered | Nicola Ciccoli | CC BY-SA 3.0 |