Dirac-Jacobi Bundles

Luca Vitagliano

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arXiv · 1502.05420

Dirac-Jacobi Bundles

Luca Vitagliano

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Abstract

We show that a suitable notion of Dirac-Jacobi structure on a generic line bundle $L$, is provided by Dirac structures in the omni-Lie algebroid of $L$. Dirac-Jacobi structures on line bundles generalize Wade's $\mathcal E^1 (M)$-Dirac structures and unify generic (i.e.~non-necessarily coorientable) precontact distributions, Dirac structures and local Lie algebras with one dimensional fibers in the sense of Kirillov (in particular, Jacobi structures in the sense of Lichnerowicz). We study the main properties of Dirac-Jacobi structures and prove that integrable Dirac-Jacobi structures on line-bundles integrate to (non-necessarily coorientable) precontact groupoids. This puts in a conceptual framework several results already available in literature for $\mathcal E^1 (M)$-Dirac structures.

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BibTeX RIS

Luca Vitagliano. 2015-02-18. Dirac-Jacobi Bundles. https://arxiv.org/abs/1502.05420

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