Double Lie algebroids and the double of a Lie bialgebroid
Differential Geometry
2007-05-23 v1
Abstract
We define a general notion of abstract double Lie algebroid. We show (1) that the double Lie algebroid of a double Lie groupoid is a double Lie algebroid in this sense; (2) that the double cotangent constructed from Lie algebroid structures on a vector bundle A and its dual A* is a double Lie algebroid if and only if (A, A*) is a Lie bialgebroid; (3) that a vacant double Lie algebroid structure is equivalent to a matched pair structure on the side Lie algebroids.
Cite
@article{arxiv.math/9808081,
title = {Double Lie algebroids and the double of a Lie bialgebroid},
author = {K. C. H. Mackenzie},
journal= {arXiv preprint arXiv:math/9808081},
year = {2007}
}
Comments
19 pages, LaTeX