Non-abelian extensions of topological Lie algebras

Details Non-abelian extensions of topological Lie algebras Non-abelian extensions of topological Lie algebras

2004-11-11

arxiv.org/abs/math/0411256v1

Mathematics

Rings and Algebras

Scientific paper

In this paper we extend and adapt several results on extensions of Lie algebras to topological Lie algebras over topological fields of characteristic zero. In particular we describe the set of equivalence classes of extensions of the Lie algebra by the Lie algebra a disjoint union of affine spaces with translation group H^2(\g,\z(\n))_{[S]}, where [S] denotes the equivalence class of the continuous outer action S \: \g \to \der \n. We also discuss topological crossed modules and explain how they are related to extensions of Lie algebras by showing that any continuous outer action gives rise to a crossed module whose obstruction class in H^3(\g,\z(\n))_S is the characteristic class of the corresponding crossed module. The correspondence between crossed modules and extensions further leads to a description of \n-extensions of \g in terms of certain \z(\n)-extensions of a Lie algebra which is an extension of \g by \n/\z(\n). We discuss several types of examples, describe applications to Lie algebras of vector fields on principal bundles, and in two appendices we describe the set of automorphisms and derivations of topological Lie algebra extensions.

Affiliated with

Also associated with

No associations

Rating

Non-abelian extensions of topological Lie algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Non-abelian extensions of topological Lie algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Non-abelian extensions of topological Lie algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-274038