Quasi-derivations and QD-algebroids
Abstract
Axioms of Lie algebroid are discussed. In particular, it is shown that a Lie QD-algebroid (i.e. a Lie algebra bracket on the C∞(M)-module ɛ of sections of a vector bundle E over a manifold M which satisfies [ X, ƒ Y] = ƒ [X, Y] + A (X, ƒ)Y for all X, Y ɛ ɛ, ƒ ɛ C∞(M), and for certain A (X, ƒ) ɛ C∞(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.
- Publication:
-
Reports on Mathematical Physics
- Pub Date:
- December 2003
- DOI:
- 10.1016/S0034-4877(03)80041-1
- arXiv:
- arXiv:math/0301234
- Bibcode:
- 2003RpMP...52..445G
- Keywords:
-
- Mathematics - Differential Geometry;
- Mathematics - Rings and Algebras;
- 17B65;
- 53D99
- E-Print:
- LaTeX, 6 pages. Minor corrections, also in the terminology. A few references added. The final version to be published in Rep. Math. Phys