The construction of 3-Lie 2-algebras
Czechoslovak Mathematical Journal, Tome 68 (2018) no. 3, pp. 711-721 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/CMJ.2018.0627-16
Classification : 17B99, 55U15
Keywords: 3-Leibniz algebras; Rota-Baxter 3-Lie algebras; 3-Lie 2-algebras
@article{10_21136_CMJ_2018_0627_16,
     author = {Wang, Chunyue and Zhang, Qingcheng},
     title = {The construction of {3-Lie} 2-algebras},
     journal = {Czechoslovak Mathematical Journal},
     pages = {711--721},
     year = {2018},
     volume = {68},
     number = {3},
     doi = {10.21136/CMJ.2018.0627-16},
     mrnumber = {3851886},
     zbl = {06986967},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0627-16/}
}
TY  - JOUR
AU  - Wang, Chunyue
AU  - Zhang, Qingcheng
TI  - The construction of 3-Lie 2-algebras
JO  - Czechoslovak Mathematical Journal
PY  - 2018
SP  - 711
EP  - 721
VL  - 68
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0627-16/
DO  - 10.21136/CMJ.2018.0627-16
LA  - en
ID  - 10_21136_CMJ_2018_0627_16
ER  - 
%0 Journal Article
%A Wang, Chunyue
%A Zhang, Qingcheng
%T The construction of 3-Lie 2-algebras
%J Czechoslovak Mathematical Journal
%D 2018
%P 711-721
%V 68
%N 3
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0627-16/
%R 10.21136/CMJ.2018.0627-16
%G en
%F 10_21136_CMJ_2018_0627_16
Wang, Chunyue; Zhang, Qingcheng. The construction of 3-Lie 2-algebras. Czechoslovak Mathematical Journal, Tome 68 (2018) no. 3, pp. 711-721. doi: 10.21136/CMJ.2018.0627-16

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

[2] Baez, J. C., Rogers, C. L.: Categorified symplectic geometry and the string Lie 2-algebra. Homology Homotopy Appl. 12 (2010), 221-236. | DOI | MR | JFM

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

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

[5] Casas, J. M., Loday, J.-L., Pirashvili, T.: Leibniz $n$-algebras. Forum Math. 14 (2002), 189-207. | DOI | MR | JFM

[6] Chen, S., Sheng, Y., Zheng, Z.: Non-abelian extensions of Lie 2-algebras. Sci. China, Math. 55 (2012), 1655-1668. | DOI | MR | JFM

[7] Lang, H., Liu, Z.: Crossed modules for Lie 2-algebras. Appl. Categ. Struct. 24 (2016), 53-78. | DOI | MR | JFM

[8] Liu, Z., Sheng, Y., Zhang, T.: Deformations of Lie 2-algebras. J. Geom. Phys. 86 (2014), 66-80. | DOI | MR | JFM

[9] Loday, J.-L., Frabetti, A., Chapoton, F., Goichot, F., eds.: Dialgebras and Related Operads. Lecture Notes in Mathematics 1763, Springer, Berlin (2001). | DOI | MR | JFM

[10] Loday, J.-L., Ronco, M.: 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), 369-398. | DOI | MR | JFM

[11] Ni, J., Wang, Y., Hou, D.: Super $\scr O $-operators of Jordan superalgebras and super Jordan Yang-Baxter equations. Front. Math. China 9 (2014), 585-599. | DOI | MR | JFM

[12] Noohi, B.: Integrating morphisms of Lie 2-algebras. Compos. Math. 149 (2013), 264-294. | DOI | MR | JFM

[13] Sheng, Y., Chen, D.: Hom-Lie 2-algebras. J. Algebra 376 (2013), 174-195. | DOI | MR | JFM

[14] Sheng, Y., Liu, Z.: From Leibniz algebras to Lie 2-algebras. Algebr. Represent. Theory 19 (2016), 1-5. | DOI | MR | JFM

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

[16] Sheng, Y., Zhu, C.: Integration of Lie 2-algebras and their morphisms. Lett. Math. Phys. 102 (2012), 223-244. | DOI | MR | JFM

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

[18] Zhou, Y., Li, Y., Sheng, Y.: 3-Lie$_{\infty}$-algebras and 3-Lie 2-algebras. J. Algebra Appl. 16 (2017), Article ID 1750171, 20 pages. | DOI | MR | JFM

Cité par Sources :