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- W2963126692 abstract "A Dirac structure is a Lagrangian subbundle of a Courant algebroid, L⊂E, which is involutive with respect to the Courant bracket. In particular, L inherits the structure of a Lie algebroid. In this paper, we introduce the more general notion of a pseudo-Dirac structure: an arbitrary subbundle, W⊂E, together with a pseudo-connection on its sections, satisfying a natural integrability condition. As a consequence of the definition, W will be a Lie algebroid. Allowing non-isotropic subbundles of E incorporates non-skew tensors and connections into Dirac geometry. Novel examples of pseudo-Dirac structures arise in the context of quasi-Poisson geometry, Lie theory, generalized Kähler geometry, and Dirac Lie groups, among others. Despite their greater generality, we show that pseudo-Dirac structures share many of the key features of Dirac structures. In particular, they behave well under composition with Courant relations." @default.
- W2963126692 created "2019-07-30" @default.
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- W2963126692 date "2014-10-01" @default.
- W2963126692 modified "2023-10-18" @default.
- W2963126692 title "Pseudo-Dirac structures" @default.
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- W2963126692 doi "https://doi.org/10.1016/j.indag.2014.07.010" @default.
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