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Keller, Frank; Waldmann, Stefan

Formal deformations of Dirac structures. (English) Zbl 1112.58018

J. Geom. Phys. 57, No. 3, 1015-1036 (2007).
Author’s abstract: In this paper we set-up a general framework for a formal deformation theory of Dirac structures. We give a parameterization of formal deformations in terms of two-forms obeying a cubic equation. The notion of equivalence is discussed in detail. We show that the obstruction for the construction of deformations order by order lies in the third Lie algebroid cohomology of the Dirac structure. However, the classification of inequivalent first order deformations is not given by the second Lie algebroid cohomology but turns out to be more complicated.
Reviewer: Witold Mozgawa (Lublin)

Cited in 6 Documents

MSC:

58H15 Deformations of general structures on manifolds
53D17 Poisson manifolds; Poisson groupoids and algebroids

Keywords:

Dirac structures; formal deformation theory; Lie algebroid cohomology; Courant algebroids; Rothstein-Poisson bracket
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\textit{F. Keller} and \textit{S. Waldmann}, J. Geom. Phys. 57, No. 3, 1015--1036 (2007; Zbl 1112.58018)
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