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Quasi-derivations and QD-algebroids

Janusz Grabowski
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Abstract

Axioms of Lie algebroid are discussed in order to review some known aspects for non-experts. In particular, it is shown that a Lie QD-algebroid (i.e. a Lie algebra bracket on the Functions(M)-module F of sections of a vector bundle E over a manifold M which satisfies [X,fY]=f[X,Y]+A(X,f)Y for all X,Y from F, all f from Functions(M), and for certain A(X,f) from Functions(M)) is a Lie algebroid if rank(E)>1, and is a local Lie algebra in the sense of Kirillov if E is a line bundle. Under a weak condition also the skew-symmetry of the bracket is relaxed.

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Janusz Grabowski. 2003-03-14. Quasi-derivations and QD-algebroids. https://doi.org/10.1016/s0034-4877(03)80041-1

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