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Bull. Korean Math. Soc. 2023; 60(3): 747-762

Online first article May 16, 2023      Printed May 31, 2023

https://doi.org/10.4134/BKMS.b220365

Copyright © The Korean Mathematical Society.

The classification of $\omega$-left-symmetric algebras in low dimensions

Zhiqi Chen, Yang Wu

Guangdong University of Technology; Nankai University

Abstract

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$\omega$-left-symmetric algebras contain left-symmetric algebras as a subclass and the commutator defines an $\omega$-Lie algebra. In this paper, we classify $\omega$-left-symmetric algebras in dimension 3 up to an isomorphism based on the classification of $\omega$-Lie algebras and the technique of Lie algebras.

Keywords: $\omega$-Lie algebra, $\omega$-left-symmetric algebra, $\omega$-isomorphism, iso\-morphism

MSC numbers: Primary 17A30, 17B60

Supported by: This work was partially supported by NNSF of China (11931009 and 12131012) and Guangdong Basic and Applied Basic Research Foundation (2023A1515010001).

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