Extensions and automorphisms of Lie algebras

Extensions and automorphisms of Lie algebras Full article

Journal

Journal of Algebra and its Applications
ISSN: 0219-4988

Output data

Year: 2017, Volume: 16, Number: 9, Article number : 1750162, Pages count : DOI: 10.1142/S0219498817501626

Tags

Automorphism of Lie algebra; cohomology of Lie algebra; extension of Lie algebras; free nilpotent Lie algebra

Authors

Bardakov V.G. ^1,2,3,4,5 , Singh M. ^1,2,3,4,5

Affiliations

1	Sobolev Institute of Mathematics, Novosibirsk, 630090, Russian Federation
2	Novosibirsk State University, Novosibirsk, 630090, Russian Federation
3	Laboratory of Quantum Topology, Chelyabinsk State University brat'Ev Kashirinykh, street 129, Chelyabinsk, 454001, Russian Federation
4	Novosibirsk State Agrarian University, Dobrolyubova street, Novosibirsk, 630039, Russian Federation
5	Indian Institute of Science Education and Research (IISER) Mohali, Sector 81 S. A. S. Nagar, P. O. Manauli, Punjab 140306, India

Let 0 A L B 0 be a short exact sequence of Lie algebras over a field F, where A is abelian. We show that the obstruction for a pair of automorphisms in Aut(A) ×Aut(B) to be induced by an automorphism in Aut(L) lies in the Lie algebra cohomology H2(B; A). 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 Aut Ln,2(1) ×Aut L n,2ab to be induced by an automorphism in Aut Ln,2, where Ln,2 is a free nilpotent Lie algebra of rank n and step 2. © 2017 World Scientific Publishing Company.

Bardakov V.G. , Singh M.
Extensions and automorphisms of Lie algebras
Journal of Algebra and its Applications. 2017. V.16. N9. 1750162 . DOI: 10.1142/S0219498817501626 WOS Scopus OpenAlex

Web of science:	WOS:000403431800002
Scopus:	2-s2.0-84990188135
OpenAlex:	W2964146207

DB	Citing
Scopus	22
OpenAlex	20
Web of science	23