Formal Deformations of Dirac Structures

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.

LaTeX 2e, 26 pages, no figures. Minor changes and improvements

References in corpus (8)

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• Derived brackets
• Variations on deformation quantization
• Courant algebroid and Lie bialgebroid contractions
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• Finite deformations from a heterotic superpotential: holomorphic Chern--Simons and an $L_{\infty }$ algebra
• Shifted derived Poisson manifolds associated with Lie pairs
• Stability of fixed points of Dirac structures
• The Deformation $L_{\infty }$ algebra of a Dirac--Jacobi structure
• Deformations of Courant Algebroids and Dirac Structures via Blended Structures