The construction of 3-Lie 2-algebras

Chunyue Wang; Qingcheng Zhang

Czechoslovak Mathematical Journal (2018)

  • Volume: 68, Issue: 3, page 711-721
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Wang, Chunyue, and Zhang, Qingcheng. "The construction of 3-Lie 2-algebras." Czechoslovak Mathematical Journal 68.3 (2018): 711-721. <http://eudml.org/doc/294323>.

@article{Wang2018,
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.},
author = {Wang, Chunyue, Zhang, Qingcheng},
journal = {Czechoslovak Mathematical Journal},
keywords = {3-Leibniz algebras; Rota-Baxter 3-Lie algebras; 3-Lie 2-algebras},
language = {eng},
number = {3},
pages = {711-721},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The construction of 3-Lie 2-algebras},
url = {http://eudml.org/doc/294323},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Wang, Chunyue
AU - Zhang, Qingcheng
TI - The construction of 3-Lie 2-algebras
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 3
SP - 711
EP - 721
AB - 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.
LA - eng
KW - 3-Leibniz algebras; Rota-Baxter 3-Lie algebras; 3-Lie 2-algebras
UR - http://eudml.org/doc/294323
ER -

References

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  1. Baez, J. C., Crans, A. S., Higher-dimensional algebra. VI. Lie 2-algebras, Theory Appl. Categ. 12 (2004), 492-538. (2004) Zbl1057.10711MR2068522
  2. Baez, J. C., Rogers, C. L., 10.4310/HHA.2010.v12.n1.a12, Homology Homotopy Appl. 12 (2010), 221-236. (2010) Zbl1277.70031MR2638872DOI10.4310/HHA.2010.v12.n1.a12
  3. Bai, R., Guo, L., Li, J., Wu, Y., 10.1063/1.4808053, J. Math. Phys. 54 (2013), 063504, 14 pages. (2013) Zbl1366.17003MR3112546DOI10.1063/1.4808053
  4. Casas, J. M., Trialgebras and Leibniz 3-algebras, Bol. Soc. Mat. Mex., III. Ser. 12 (2006), 165-178. (2006) Zbl1151.17001MR2292981
  5. Casas, J. M., Loday, J.-L., Pirashvili, T., 10.1515/form.2002.009, Forum Math. 14 (2002), 189-207. (2002) Zbl1037.17002MR1880911DOI10.1515/form.2002.009
  6. Chen, S., Sheng, Y., Zheng, Z., 10.1007/s11425-012-4398-7, Sci. China, Math. 55 (2012), 1655-1668. (2012) Zbl1280.17026MR2955249DOI10.1007/s11425-012-4398-7
  7. Lang, H., Liu, Z., 10.1007/s10485-015-9389-8, Appl. Categ. Struct. 24 (2016), 53-78. (2016) Zbl06541802MR3448428DOI10.1007/s10485-015-9389-8
  8. Liu, Z., Sheng, Y., Zhang, T., 10.1016/j.geomphys.2014.07.020, J. Geom. Phys. 86 (2014), 66-80. (2014) Zbl1362.17032MR3282312DOI10.1016/j.geomphys.2014.07.020
  9. Loday, J.-L., Frabetti, A., Chapoton, F., Goichot, F., eds., 10.1007/b80864, Lecture Notes in Mathematics 1763, Springer, Berlin (2001). (2001) Zbl0970.00010MR1864390DOI10.1007/b80864
  10. Loday, J.-L., Ronco, M., 10.1090/conm/346/06296, Homotopy Theory: Relations with Algebraic Geometry, Group Cohomology, and Algebraic -Theory Conf. on algebraic topology, Northwestern University, Evanston, Contemporary Mathematics 346, American Mathematical Society, Providence (2004), 369-398. (2004) Zbl1065.18007MR2066507DOI10.1090/conm/346/06296
  11. Ni, J., Wang, Y., Hou, D., 10.1007/s11464-014-0339-9, Front. Math. China 9 (2014), 585-599. (2014) Zbl1333.17025MR3195837DOI10.1007/s11464-014-0339-9
  12. Noohi, B., 10.1112/S0010437X1200067X, Compos. Math. 149 (2013), 264-294. (2013) Zbl1315.22023MR3020309DOI10.1112/S0010437X1200067X
  13. Sheng, Y., Chen, D., 10.1016/j.jalgebra.2012.11.032, J. Algebra 376 (2013), 174-195. (2013) Zbl1281.17034MR3003723DOI10.1016/j.jalgebra.2012.11.032
  14. Sheng, Y., Liu, Z., 10.1007/s10468-015-9556-5, Algebr. Represent. Theory 19 (2016), 1-5. (2016) Zbl06563849MR3465885DOI10.1007/s10468-015-9556-5
  15. Sheng, Y., Liu, Z., Zhu, C., 10.1016/j.geomphys.2010.11.005, J. Geom. Phys. 61 (2011), 560-575. (2011) Zbl1242.17026MR2746137DOI10.1016/j.geomphys.2010.11.005
  16. Sheng, Y., Zhu, C., 10.1007/s11005-012-0578-1, Lett. Math. Phys. 102 (2012), 223-244. (2012) Zbl1335.17008MR2984165DOI10.1007/s11005-012-0578-1
  17. Sheng, Y., Zhu, C., 10.1142/S0219887812500430, Int. J. Geom. Methods Mod. Phys. 9 (2012), 1250043, 31 pages. (2012) Zbl1277.17012MR2948862DOI10.1142/S0219887812500430
  18. Zhou, Y., Li, Y., Sheng, Y., 10.1142/S0219498817501717, J. Algebra Appl. 16 (2017), Article ID 1750171, 20 pages. (2017) Zbl06745725MR3661638DOI10.1142/S0219498817501717

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