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Added:
A bijective correspondence between Lie algebroid structures, homological vector fields of degree 1, and odd linear Poisson structures is established in the paper
added pointer to today’s
I corrected the mistake where it says that the tangent map of the anchor preserves the bracket… it is actually the anchor itself that preserved the bracket (see for instance M. Cranic, R.L. Fernandes, I. Marcut Lectures on Poisson Geometry, AMS Graduate Texts in Mathematics 217, Proposition 9.2).
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