On the axioms of Leibniz algebroids associated to Nambu-Poisson manifolds

S. Srinivas Rau; T. Shreecharan

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arXiv · 1510.07544

On the axioms of Leibniz algebroids associated to Nambu-Poisson manifolds

S. Srinivas Rau·T. Shreecharan

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Abstract

Let $E \rightarrow M$ be a smooth vector bundle with a bilinear product on $\Gamma(E)$ satisfying the Jacobi identity. Assuming only the existence of an anchor map $\mathfrak{a}$ we show that $\mathfrak{a}([X,Y]) = [\mathfrak{a}X,\mathfrak{a}Y]_c$. This gives the redundancy of the homomorphism condition in the definition of Leibniz algebroid; in particular if it arises from a Nambu-Poisson manifold.

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BibTeX RIS

S. Srinivas Rau, T. Shreecharan. 2015-10-22. On the axioms of Leibniz algebroids associated to Nambu-Poisson manifolds. https://arxiv.org/abs/1510.07544

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