MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question
Try Atyiah algebroid. – Vít Tuček Jan 31 '12 at 22:13

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.

share|cite|improve this answer

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

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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