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Acta Mathematica Sinica, English Series

, Volume 34, Issue 6, pp 933–946 | Cite as

Restricted Lie 2-algebras

  • Yan Tan
  • Zhi Xiang Wu
Article

Abstract

In this article, we introduce the notions of restricted Lie 2-algebras and crossed modules of restricted Lie algebras, and give a series of examples of restricted Lie 2-algebras. We also construct restricted Lie 2-algebras from A(m)-algebras, restricted Leibniz algebras, restricted right-symmetric algebras. Finally, we prove that there is a one-to-one correspondence between strict restricted Lie 2-algebras and crossed modules of restricted Lie algebras.

Keywords

Restricted Lie 2-algebra crossed module of restricted Lie algebra A(m)-algebra restricted Leibniz algebra restricted right-symmetric algebra 

MR(2010) Subject Classification

17B50 55U15 

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Notes

Acknowledgements

The authors would like to thank the referees for their careful reading and helpful comments and suggestions on this paper.

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesZhejiang UniversityHangzhouP. R. China

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