Extensions and automorphisms of Lie algebras-Reference-Cited by-同舟云学术

Extensions and automorphisms of Lie algebras

Published:2016-09-09 Issue:09 Volume:16 Page:1750162
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

Bardakov Valeriy G.¹²³⁴⁵,Singh Mahender¹²³⁴⁵

Affiliation:

1. Sobolev Institute of Mathematics, Novosibirsk 630090, Russia

2. Novosibirsk State University, Novosibirsk 630090, Russia

3. Laboratory of Quantum Topology, Chelyabinsk, State University Brat’ev Kashirinykh street 129, Chelyabinsk 454001, Russia

4. Novosibirsk State Agrarian University, Dobrolyubova street, 160 Novosibirsk, 630039, Russia

5. Indian Institute of Science Education and Research (IISER) Mohali, Sector 81, S. A. S. Nagar, P. O. Manauli, Punjab 140306, India

Abstract

Let [Formula: see text] be a short exact sequence of Lie algebras over a field [Formula: see text], where [Formula: see text] is abelian. We show that the obstruction for a pair of automorphisms in [Formula: see text] to be induced by an automorphism in [Formula: see text] lies in the Lie algebra cohomology [Formula: see text]. 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 [Formula: see text] to be induced by an automorphism in [Formula: see text], where [Formula: see text] is a free nilpotent Lie algebra of rank [Formula: see text] and step [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498817501626

Reference11 articles.

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2. On Semi-Simple Automorphisms of Lie Algebras

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