3
$\begingroup$

I am wondering whether there is a Lie algebraic version of principal bundle for Lie group over a given manifold $M$. The first thing I try to think of is group cocycle picture of principal bundle.

$\endgroup$
1
  • 3
    $\begingroup$ Try Atyiah algebroid. $\endgroup$ Jan 31, 2012 at 22:13

2 Answers 2

4
$\begingroup$

A very comprehensive source is:

MR2157566 Mackenzie, Kirill C. H. General theory of Lie groupoids and Lie algebroids. London Mathematical Society Lecture Note Series, 213. Cambridge University Press, Cambridge, 2005. xxxviii+501 pp.

Starting from the total space, there is also the notion of the action of a Lie algebra on a manifold, which one can extend to a Lie group action by enlarging the manifold (and loosing Hausdorff in general), see here.

$\endgroup$
0
$\begingroup$

Building upon Peter's answer, An Atiyah algebroid, or transitive Lie algebroid is one answer to your question.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.