Quasi-derivations and QD-algebroids
Differential Geometry
2009-11-10 v2 Rings and Algebras
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.
Cite
@article{arxiv.math/0301234,
title = {Quasi-derivations and QD-algebroids},
author = {Janusz Grabowski},
journal= {arXiv preprint arXiv:math/0301234},
year = {2009}
}
Comments
LaTeX, 6 pages. Minor corrections, also in the terminology. A few references added. The final version to be published in Rep. Math. Phys