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On Extensions of Some Classes of Algebras

  • Isamiddin Rakhimov
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 264)

Abstract

The paper consists of three parts. In the first part we discuss on extensions of Lie algebras and their importance in Physics. Then we deal with the extensions of some classes of algebras with one binary operation. The third part is devoted to the study of extensions of two classes of algebras, possessing two algebraic operations, called dialgebras. In all the cases we propose 2-cocycles and respective extensions. The motivation to study the extensions is to use them further for the classification problem of the classes algebras considered in low dimensional cases.

Keywords

Lie algebra Associative algebra Pre-Lie algebra Leibniz algebra Zinbiel algebra Dialgebra 

Notes

Acknowledgements

The author would like to thank the referee for the comments made. The research was supported by FRGS Grant 01-01-16-1869FR, MOHE, Malaysia.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Institute for Mathematical Research (INSPEM)Universiti Putra MalaysiaSerdangMalaysia

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