Twisted Jacobi manifolds, twisted Dirac-Jacobi structures and quasi-Jacobi bialgebroids

Abstract

We study twisted Jacobi manifolds, a concept that we had introduced in a previous Note. Twisted Jacobi manifolds can be characterized using twisted Dirac-Jacobi, which are sub-bundles of Courant-Jacobi algebroids. We show that each twisted Jacobi manifold has an associated Lie algebroid with a 1-cocycle. We introduce the notion of quasi-Jacobi bialgebroid and we prove that each twisted Jacobi manifold has a quasi-Jacobi bialgebroid canonically associated. Moreover, the double of a quasi-Jacobi bialgebroid is a Courant-Jacobi algebroid. Several examples of twisted Jacobi manifolds and twisted Dirac-Jacobi structures are presented.

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• Derived brackets
• WZW-Poisson manifolds
• Generalized Lie bialgebroids and Jacobi structures
• Jacobi structures revisited
• The graded Jacobi algebras and (co)homology
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Cited by in corpus (8)

• Gauged sigma-models with nonclosed 3-form and twisted Jacobi structures
• On Locally Conformally Cosymplectic Hamiltonian Dynamics and Hamilton-Jacobi Theory
• On the geometric quantization of twisted Poisson manifolds
• On Jacobi quasi-Nijenhuis algebroids and Courant-Jacobi algebroid morphisms
• On quasi-Jacobi and Jacobi-quasi bialgebroids
• Jacobi quasi-Nijenhuis Algebroids
• Jacobi Geometry and Hamiltonian Mechanics: the Unit-Free Approach
• Jacobi Sigma Models and Twisted Jacobi Structures