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Simple \(\omega \)-Lie Algebras and 4-Dimensional \(\omega \)-Lie Algebras Over \({\mathbb {C}}\)

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Abstract

In this paper, we study simple \(\omega \)-Lie algebras and 4-dimensional \(\omega \)-Lie algebras over the field of complex numbers. We provide an approach to classify all 4-dimensional non-Lie complex \(\omega \)-Lie algebras. We prove that any non-Lie finite-dimensional simple \(\omega \)-Lie algebra has dimension 3. A complete list of all non-Lie complex simple \(\omega \)-Lie algebras is also derived.

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Acknowledgments

We would like to thank the anonymous referees for their comments on the first version of this paper. We are grateful to China Scholarship Council for the overseas scholarships to visit Queen’s University where this work started. We thank Yaqing Sun and Yonggang Lu for their help. We also thank the staff of Department of Mathematics and Statistics of Queen’s for providing a comfortable working circumstance. This work was supported partially by NSF of China (11301061, 11401087) and JPSTD (20130522098JH, 20140520052JH).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, People’s Republic of China

    Yin Chen & Runxuan Zhang

Authors
  1. Yin Chen
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  2. Runxuan Zhang
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Correspondence to Runxuan Zhang.

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Communicated by Rosihan M. Ali.

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Chen, Y., Zhang, R. Simple \(\omega \)-Lie Algebras and 4-Dimensional \(\omega \)-Lie Algebras Over \({\mathbb {C}}\) . Bull. Malays. Math. Sci. Soc. 40, 1377–1390 (2017). https://doi.org/10.1007/s40840-015-0120-6

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  • DOI: https://doi.org/10.1007/s40840-015-0120-6

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