Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
3-Leibniz algebras; Rota-Baxter 3-Lie algebras; 3-Lie 2-algebras
3-Leibniz algebras; Rota-Baxter 3-Lie algebras; 3-Lie 2-algebras
Summary:
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.
References:
[1] Baez, J. C., Crans, A. S.: Higher-dimensional algebra. VI. Lie 2-algebras. Theory Appl. Categ. 12 (2004), 492-538. MR 2068522 | Zbl 1057.10711
[2] Baez, J. C., Rogers, C. L.: Categorified symplectic geometry and the string Lie 2-algebra. Homology Homotopy Appl. 12 (2010), 221-236. DOI 10.4310/HHA.2010.v12.n1.a12 | MR 2638872 | Zbl 1277.70031
[3] Bai, R., Guo, L., Li, J., Wu, Y.: Rota-Baxter 3-Lie algebras. J. Math. Phys. 54 (2013), 063504, 14 pages. DOI 10.1063/1.4808053 | MR 3112546 | Zbl 1366.17003
[4] Casas, J. M.: Trialgebras and Leibniz 3-algebras. Bol. Soc. Mat. Mex., III. Ser. 12 (2006), 165-178. MR 2292981 | Zbl 1151.17001
[5] Casas, J. M., Loday, J.-L., Pirashvili, T.: Leibniz $n$-algebras. Forum Math. 14 (2002), 189-207. DOI 10.1515/form.2002.009 | MR 1880911 | Zbl 1037.17002
[6] Chen, S., Sheng, Y., Zheng, Z.: Non-abelian extensions of Lie 2-algebras. Sci. China, Math. 55 (2012), 1655-1668. DOI 10.1007/s11425-012-4398-7 | MR 2955249 | Zbl 1280.17026
[7] Lang, H., Liu, Z.: Crossed modules for Lie 2-algebras. Appl. Categ. Struct. 24 (2016), 53-78. DOI 10.1007/s10485-015-9389-8 | MR 3448428 | Zbl 06541802
[8] Liu, Z., Sheng, Y., Zhang, T.: Deformations of Lie 2-algebras. J. Geom. Phys. 86 (2014), 66-80. DOI 10.1016/j.geomphys.2014.07.020 | MR 3282312 | Zbl 1362.17032
[9] Loday, J.-L., Frabetti, A., Chapoton, F., Goichot, F., eds.: Dialgebras and Related Operads. Lecture Notes in Mathematics 1763, Springer, Berlin (2001). DOI 10.1007/b80864 | MR 1864390 | Zbl 0970.00010
[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 10.1090/conm/346/06296 | MR 2066507 | Zbl 1065.18007
[11] Ni, J., Wang, Y., Hou, D.: Super $\scr O $-operators of Jordan superalgebras and super Jordan Yang-Baxter equations. Front. Math. China 9 (2014), 585-599. DOI 10.1007/s11464-014-0339-9 | MR 3195837 | Zbl 1333.17025
[12] Noohi, B.: Integrating morphisms of Lie 2-algebras. Compos. Math. 149 (2013), 264-294. DOI 10.1112/S0010437X1200067X | MR 3020309 | Zbl 1315.22023
[13] Sheng, Y., Chen, D.: Hom-Lie 2-algebras. J. Algebra 376 (2013), 174-195. DOI 10.1016/j.jalgebra.2012.11.032 | MR 3003723 | Zbl 1281.17034
[14] Sheng, Y., Liu, Z.: From Leibniz algebras to Lie 2-algebras. Algebr. Represent. Theory 19 (2016), 1-5. DOI 10.1007/s10468-015-9556-5 | MR 3465885 | Zbl 06563849
[15] Sheng, Y., Liu, Z., Zhu, C.: Omni-Lie 2-algebras and their Dirac structures. J. Geom. Phys. 61 (2011), 560-575. DOI 10.1016/j.geomphys.2010.11.005 | MR 2746137 | Zbl 1242.17026
[16] Sheng, Y., Zhu, C.: Integration of Lie 2-algebras and their morphisms. Lett. Math. Phys. 102 (2012), 223-244. DOI 10.1007/s11005-012-0578-1 | MR 2984165 | Zbl 1335.17008
[17] Sheng, Y., Zhu, C.: Integration of semidirect product Lie 2-algebras. Int. J. Geom. Methods Mod. Phys. 9 (2012), 1250043, 31 pages. DOI 10.1142/S0219887812500430 | MR 2948862 | Zbl 1277.17012
[18] Zhou, Y., Li, Y., Sheng, Y.: 3-Lie$_{\infty}$-algebras and 3-Lie 2-algebras. J. Algebra Appl. 16 (2017), Article ID 1750171, 20 pages. DOI 10.1142/S0219498817501717 | MR 3661638 | Zbl 06745725
Search
Partner of
