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Article overview
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The graded Jacobi algebras and (co)homology | Janusz Grabowski
; Giuseppe Marmo
; | Date: |
2 Jul 2002 | Journal: | J. Phys. A: Math. Gen. 36 (2003), 161-181 | Subject: | Differential Geometry; Mathematical Physics MSC-class: 17B63; 53D99; 17B66 | math.DG math-ph math.MP | Abstract: | 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. | Source: | arXiv, math.DG/0207017 | Services: | Forum | Review | PDF | Favorites |
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