Quasi-derivations and QD-algebroids
arXiv:math/0301234 · doi:10.1016/S0034-4877(03)80041-1
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.
LaTeX, 6 pages. Minor corrections, also in the terminology. A few references added. The final version to be published in Rep. Math. Phys
References in corpus (1)
Cited by in corpus (20)
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