Skip to main content
SpringerLink
Log in

The construction of 3-Lie 2-algebras

  • Published:
Czechoslovak Mathematical Journal Aims and scope Submit manuscript

Abstract

We construct a 3-Lie 2-algebra from a 3-Leibniz algebra and a Rota-Baxter 3-Lie algebra. Moreover, we give some examples of 3-Leibniz algebras.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. C. Baez, A. S. Crans: Higher-dimensional algebra. VI. Lie 2-algebras. Theory Appl. Categ. 12 (2004), 492–538.

    MathSciNet  MATH  Google Scholar 

  2. J. C. Baez, C. L. Rogers: Categorified symplectic geometry and the string Lie 2-algebra. Homology Homotopy Appl. 12 (2010), 221–236.

    Article  MathSciNet  MATH  Google Scholar 

  3. R. Bai, L. Guo, J. Li, Y. Wu: Rota-Baxter 3-Lie algebras. J. Math. Phys. 54 (2013), 063504, 14 pages.

    Article  MathSciNet  MATH  Google Scholar 

  4. J. M. Casas: Trialgebras and Leibniz 3-algebras. Bol. Soc. Mat. Mex., III. Ser. 12 (2006), 165–178.

    MathSciNet  MATH  Google Scholar 

  5. J. M. Casas, J.-L. Loday, T. Pirashvili: Leibniz n-algebras. Forum Math. 14 (2002), 189–207.

    Article  MathSciNet  MATH  Google Scholar 

  6. S. Chen, Y. Sheng, Z. Zheng: Non-abelian extensions of Lie 2-algebras. Sci. China, Math. 55 (2012), 1655–1668.

    Article  MathSciNet  MATH  Google Scholar 

  7. H. Lang, Z. Liu: Crossed modules for Lie 2-algebras. Appl. Categ. Struct. 24 (2016), 53–78.

    Article  MathSciNet  MATH  Google Scholar 

  8. Z. Liu, Y. Sheng, T. Zhang: Deformations of Lie 2-algebras. J. Geom. Phys. 86 (2014), 66–80.

    Article  MathSciNet  MATH  Google Scholar 

  9. J.-L. Loday, A. Frabetti, F. Chapoton, F. Goichot, eds.: Dialgebras and Related Operads. Lecture Notes in Mathematics 1763, Springer, Berlin, 2001.

    Google Scholar 

  10. J.-L. Loday, M. Ronco: Trialgebras and families of polytopes. Homotopy Theory: Relations with Algebraic Geometry, Group Cohomology, and Algebraic K-Theory. Conf. on algebraic topology, Northwestern University, Evanston, Contemporary Mathematics 346, American Mathematical Society, Providence, 2004, pp. 369–398.

    Google Scholar 

  11. J. Ni, Y. Wang, D. Hou: Super O-operators of Jordan superalgebras and super Jordan Yang-Baxter equations. Front. Math. China 9 (2014), 585–599.

    Article  MathSciNet  MATH  Google Scholar 

  12. B. Noohi: Integrating morphisms of Lie 2-algebras. Compos. Math. 149 (2013), 264–294.

    Article  MathSciNet  MATH  Google Scholar 

  13. Y. Sheng, D. Chen: Hom-Lie 2-algebras. J. Algebra 376 (2013), 174–195.

    Article  MathSciNet  MATH  Google Scholar 

  14. Y. Sheng, Z. Liu: From Leibniz algebras to Lie 2-algebras. Algebr. Represent. Theory 19 (2016), 1–5.

    Article  MathSciNet  MATH  Google Scholar 

  15. Y. Sheng, Z. Liu, C. Zhu: Omni-Lie 2-algebras and their Dirac structures. J. Geom. Phys. 61 (2011), 560–575.

    Article  MathSciNet  MATH  Google Scholar 

  16. Y. Sheng, C. Zhu: Integration of Lie 2-algebras and their morphisms. Lett. Math. Phys. 102 (2012), 223–244.

    Article  MathSciNet  MATH  Google Scholar 

  17. Y. Sheng, C. Zhu: Integration of semidirect product Lie 2-algebras. Int. J. Geom. Methods Mod. Phys. 9 (2012), 1250043, 31 pages.

    Article  MathSciNet  MATH  Google Scholar 

  18. Y. Zhou, Y. Li, Y. Sheng: 3-Lie8-algebras and 3-Lie 2-algebras. J. Algebra Appl. 16 (2017), Article ID 1750171, 20 pages.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Jilin University, No. 2699 Qianjin Street, Changchun, Jilin, 130012, China

    Chunyue Wang

  2. Department of Mathematics, Jilin Engineering Normal University, 3050 Kaixuan Rd., Changchun, Jilin, 130052, China

    Chunyue Wang

  3. School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin, 130024, China

    Qingcheng Zhang

Authors
  1. Chunyue Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qingcheng Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chunyue Wang.

Additional information

The research has been supported by Science and Technology Research Fund of Jilin Province (2016111).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, C., Zhang, Q. The construction of 3-Lie 2-algebras. Czech Math J 68, 711–721 (2018). https://doi.org/10.21136/CMJ.2018.0627-16

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.21136/CMJ.2018.0627-16

Keywords

MSC 2010

Search

Navigation