Dirac generating operators and Manin triples


Given a pair of Lie algebroid structures on a vector bundle A (over M) and its dual A∗, and provided the A∗-module L = (∧A ⊗ ∧T ∗M) 1 2 exists, there exists a canonically defined differential operator D̆ on Γ(∧A ⊗ L ). We prove that the pair (A,A∗) constitutes a Lie bialgebroid if, and only if, D̆ is a Dirac generating operator as defined by Alekseev & Xu… (More)


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