Quasi-derivations and QD-algebroids

Details Quasi-derivations and QD-algebroids Quasi-derivations and QD-algebroids

2003-01-21

arxiv.org/abs/math/0301234v2

Rep. Math. Phys. 32 (2003), 445-451.

Mathematics

Differential Geometry

LaTeX, 6 pages. Minor corrections, also in the terminology. A few references added. The final version to be published in Rep.

Scientific paper

10.1016/S0034-4877(03)80041-1

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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