The graded Jacobi algebras and (co)homology
| dc.creator | Grabowski, Janusz | |
| dc.creator | Marmo, Giuseppe | |
| dc.date | 2002-07-02 | |
| dc.date | 2002-11-18 | |
| dc.date.accessioned | 2026-07-07T10:38:18Z | |
| dc.date.available | 2026-07-07T10:38:18Z | |
| dc.description | Jacobi algebroids (i.e. `Jacobi versions' of Lie algebroids) are studied in the context of graded Jacobi brackets on graded commutative algebras. This unifies varios concepts of graded Lie structures in geometry and physics. A method of describing such structures by classical Lie algebroids via certain gauging (in the spirit of E.Witten's gauging of exterior derivative) is developed. One constructs a corresponding Cartan differential calculus (graded commutative one) in a natural manner. This, in turn, gives canonical generating operators for triangular Jacobi algebroids. One gets, in particular, the Lichnerowicz-Jacobi homology operators associated with classical Jacobi structures. Courant-Jacobi brackets are obtained in a similar way and use to define an abstract notion of a Courant-Jacobi algebroid and Dirac-Jacobi structure. All this offers a new flavour in understanding the Batalin-Vilkovisky formalism. | |
| dc.description | 20 pages, a few typos corrected; final version to be published in J. Phys. A: Math. Gen | |
| dc.identifier | https://arxiv.org/abs/math/0207017 | |
| dc.identifier | http://arxiv.org/abs/math/0207017 | |
| dc.identifier | J.Phys.A36:161-181,2003 | |
| dc.identifier | doi:10.1088/0305-4470/36/1/311 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/180673 | |
| dc.subject | Differential Geometry | |
| dc.subject | Mathematical Physics | |
| dc.subject | 17B63; 53D99; 17B66 | |
| dc.title | The graded Jacobi algebras and (co)homology | |
| dc.type | text |