Locally Conformal Dirac Structures and Infinitesimal Automorphisms

Research output: Contribution to journalArticle

5 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)295-310
Number of pages16
JournalCommunications In Mathematical Physics
Volume246
Issue number2
DOIs
StatePublished - Apr 1 2004

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Dirac Structures
Conformal Structure
automorphisms
Paul Adrien Maurice Dirac
bundles
Automorphisms
Bundle
algebra
Lie Algebra
quotients
Lie Algebroids
Covering Map
Symplectic Manifold
Smooth Manifold
coverings
Homomorphism
Jacobi
Subalgebra
Quotient

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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

In: Communications In Mathematical Physics, Vol. 246, No. 2, 01.04.2004, p. 295-310.

Research output: Contribution to journalArticle

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