2003/01/31 by Janusz Grabowski · 2 citations
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Rings, Modules, and Algebras #math.DG #math.RA #msc:17B65 #msc:53D99
paper · pdf · doi:10.1016/s0034-4877(03)80041-1
published as Rep. Math. Phys. 32 (2003), 445-451. · LaTeX, 6 pages. Minor corrections, also in the terminology. A few references added. The final version to be published in Rep. Math. Phys
arxiv created 2003/03/14 · openalex publication_date 2003/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.