### Abstract

We study the main properties of locally conformal Dirac bundles, which include Dirac structures on a manifold and locally conformal symplectic manifolds. It is proven that certain locally conformal Dirac bundles induce Jacobi structures on quotient manifolds. Furthermore we show that, given a locally conformal Dirac bundle over a smooth manifold M, there is a Lie homomorphism between a subalgebra of the Lie algebra of infinitesimal automorphisms and the Lie algebra of admissible functions. We also show that Dirac manifolds can be obtained from locally conformal Dirac bundles by using an appropriate covering map. Finally, we extend locally conformal Dirac bundles to the context of Lie algebroids.

Original language | English (US) |
---|---|

Pages (from-to) | 295-310 |

Number of pages | 16 |

Journal | Communications In Mathematical Physics |

Volume | 246 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1 2004 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

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*Communications In Mathematical Physics*, vol. 246, no. 2, pp. 295-310. https://doi.org/10.1007/s00220-004-1047-1

**Locally Conformal Dirac Structures and Infinitesimal Automorphisms.** / Wade, Aissa.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Locally Conformal Dirac Structures and Infinitesimal Automorphisms

AU - Wade, Aissa

PY - 2004/4/1

Y1 - 2004/4/1

N2 - We study the main properties of locally conformal Dirac bundles, which include Dirac structures on a manifold and locally conformal symplectic manifolds. It is proven that certain locally conformal Dirac bundles induce Jacobi structures on quotient manifolds. Furthermore we show that, given a locally conformal Dirac bundle over a smooth manifold M, there is a Lie homomorphism between a subalgebra of the Lie algebra of infinitesimal automorphisms and the Lie algebra of admissible functions. We also show that Dirac manifolds can be obtained from locally conformal Dirac bundles by using an appropriate covering map. Finally, we extend locally conformal Dirac bundles to the context of Lie algebroids.

AB - We study the main properties of locally conformal Dirac bundles, which include Dirac structures on a manifold and locally conformal symplectic manifolds. It is proven that certain locally conformal Dirac bundles induce Jacobi structures on quotient manifolds. Furthermore we show that, given a locally conformal Dirac bundle over a smooth manifold M, there is a Lie homomorphism between a subalgebra of the Lie algebra of infinitesimal automorphisms and the Lie algebra of admissible functions. We also show that Dirac manifolds can be obtained from locally conformal Dirac bundles by using an appropriate covering map. Finally, we extend locally conformal Dirac bundles to the context of Lie algebroids.

UR - http://www.scopus.com/inward/record.url?scp=2142662871&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2142662871&partnerID=8YFLogxK

U2 - 10.1007/s00220-004-1047-1

DO - 10.1007/s00220-004-1047-1

M3 - Article

AN - SCOPUS:2142662871

VL - 246

SP - 295

EP - 310

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -