Simultaneous deformations of a Lie algebroid and its Lie subalgebroid

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Abstract

Deformation problem is an interesting problem in mathematical physics. In this paper, we show that the deformations of a Lie algebroid are governed by a differential graded Lie algebra; and under certain regularity assumptions, an L-algebra can be constructed to govern the deformations of its Lie subalgebroid. Furthermore, by applying Y. Frégier and M. Zambon's result (0000, Thm. 3), these structures can be combined together to govern the simultaneous deformations. Applications of our results include deformations of a foliation, deformations of a Lie subalgebra, deformations of a complex structure, and deformations of a homomorphism of Lie algebroids.

Original languageEnglish (US)
Pages (from-to)8-29
Number of pages22
JournalJournal of Geometry and Physics
Volume84
DOIs
StatePublished - Oct 2014

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Geometry and Topology

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