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- Title
Extensions and automorphisms of Lie algebras.
- Authors
Bardakov, Valeriy G.; Singh, Mahender
- Abstract
Let be a short exact sequence of Lie algebras over a field , where is abelian. We show that the obstruction for a pair of automorphisms in to be induced by an automorphism in lies in the Lie algebra cohomology . As a consequence, we obtain a four term exact sequence relating automorphisms, derivations and cohomology of Lie algebras. We also obtain a more explicit necessary and sufficient condition for a pair of automorphisms in to be induced by an automorphism in , where is a free nilpotent Lie algebra of rank and step .
- Subjects
GROUP extensions (Mathematics); AUTOMORPHISMS; LIE algebras; MATHEMATICAL sequences; ISOMORPHISM (Mathematics)
- Publication
Journal of Algebra & Its Applications, 2017, Vol 16, Issue 9, p-1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498817501626