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• W2963761345 abstract "Omni-Lie algebroids are generalizations of Alan Weinstein's omni-Lie algebras. A Dirac structure in an omni-Lie algebroid 𝔇E ⊕ 𝔍E is necessarily a Lie algebroid together with a representation on E. We study the geometry underlying these Dirac structures in the light of reduction theory. In particular, we prove that there is a one-to-one correspondence between reducible Dirac structures and projective Lie algebroids in [Formula: see text]; we establish the relation between the normalizer N L of a reducible Dirac structure L and the derivation algebra Der (b (L)) of the projective Lie algebroid b(L); we study the cohomology group H • (L, ρL ) and the relation between N L and H 1 (L, ρ L ); we describe Lie bialgebroids using the adjoint representation; we study the deformation of a Dirac structure L, which is related with H 2 (L, ρ L )." @default.
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• W2963761345 date "2011-08-01" @default.
• W2963761345 modified "2023-10-16" @default.
• W2963761345 title "DIRAC STRUCTURES OF OMNI-LIE ALGEBROIDS" @default.
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• W2963761345 doi "https://doi.org/10.1142/s0129167x11007215" @default.
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