English

Extensions of Lie algebras

Differential Geometry 2007-05-23 v3 Representation Theory

Abstract

We review (non-abelian) extensions of a given Lie algebra, identify a 3-dimensional cohomological obstruction to the existence of extensions. A striking analogy to the setting of covariant exterior derivatives, curvature, and the Bianchi identity in differential geometry is spelled out. In the new version references added: Most of the results are known. So this paper will not be submitted to a journal, it can be regarded as a review paper.

Keywords

Cite

@article{arxiv.math/0005042,
  title  = {Extensions of Lie algebras},
  author = {Dmitri Alekseevsky and Peter W. Michor and Wolfgang Ruppert},
  journal= {arXiv preprint arXiv:math/0005042},
  year   = {2007}
}

Comments

AmSTeX + diag.tex, 9 pages In the new version references added: Most of the results are known. The last (wrong) statement omitted. So this paper will not be submitted to a journal, it can be regarded as a review paper

R2 v1 2026-07-22T16:32:31.902Z