Omni-Lie Algebras
| dc.creator | Weinstein, Alan | |
| dc.date | 1999-12-22 | |
| dc.date | 2000-02-01 | |
| dc.date.accessioned | 2026-07-07T05:32:27Z | |
| dc.date.available | 2026-07-07T05:32:27Z | |
| dc.description | We show that the space R^n x gl(n,R) with a certain antisymmetric bracket operation contains all n-dimensional Lie algebras. The bracket does not satisfy the Jacobi identity, but it does satisfy it for subalgebras which are isotropic under a certain symmetric bilinear form with values in R^n. We ask what the corresponding "group-like" object should be. The bracket may be obtained by linearizing at a point the bracket on TM + T*M introduced by T. Courant for the definition of Dirac structures, a notion which encompasses Poisson structures, closed 2-forms, and foliations. | |
| dc.description | 8 pages, minor corrections and announcement of further results | |
| dc.identifier | https://arxiv.org/abs/math/9912190 | |
| dc.identifier | http://arxiv.org/abs/math/9912190 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79661 | |
| dc.subject | Representation Theory | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 17B99; 17B62,53D17 | |
| dc.title | Omni-Lie Algebras | |
| dc.type | text |