A note on optimal systems of certain low-dimensional Lie algebras

Manjit Singh; Rajesh Kumar Gupta

doi:10.1515/ijnsns-2017-0181

Article

A note on optimal systems of certain low-dimensional Lie algebras

Manjit Singh and Rajesh Kumar Gupta

Published/Copyright: December 16, 2020

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From the journal International Journal of Nonlinear Sciences and Numerical Simulation Volume 22 Issue 2

Abstract

Optimal classifications of Lie algebras of some well-known equations under their group of inner automorphism are re-considered. By writing vector fields of some known Lie algebras in the abstract format, we have proved that there exist explicit isomorphism between Lie algebras and sub-algebras which have already been classified. The isomorphism between Lie algebras is useful in the sense that the classifications of sub-algebras of dimension ≤4 have previously been carried out in literature. These already available classifications can be used to write classification of any Lie algebra of dimension ≤4. As an example, the explicit isomorphism between Lie algebra of variant Boussinesq system and sub-algebra A 3,5 1 / 2 is proved, and subsequently, optimal sub-algebras up to dimension four are obtained. Besides this, some other examples of Lie algebras are also considered for explicit isomorphism.

Keywords: isomorphic Lie algebras; Lie algebra classification; normalizer; optimal system

MSC 2010: 22E15; 2E60; 70G65

Corresponding author: Manjit Singh, Yadavindra College of Engineering, Punjabi University Guru Kashi Campus, Talwandi Sabo, 151302, Punjab, India, E-mail: manjitcsir@gmail.com

Funding source: University Grants Commission

Award Identifier / Grant number: F. 30-105/2016 (SA-II)

Acknowledgements

Rajesh Kumar Gupta thanks the University Grant Commission for sponsoring this research under Research Award Scheme (F. 30-105/2016 (SA-II)).

Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: The research was funded by University Grant Commission (F. 30-105/2016 (SA-II)).
Conflict of interest statement: The authors declare no conflicts of interest.

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Received: 2017-08-20

Accepted: 2020-11-19

Published Online: 2020-12-16

Published in Print: 2021-04-27

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Articles in the same Issue

https://doi.org/10.1515/ijnsns-2017-0181

Keywords for this article

isomorphic Lie algebras; Lie algebra classification; normalizer; optimal system