Title:
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The construction of 3-Lie 2-algebras (English) |
Author:
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Wang, Chunyue |
Author:
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Zhang, Qingcheng |
Language:
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English |
Journal:
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Czechoslovak Mathematical Journal |
ISSN:
|
0011-4642 (print) |
ISSN:
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1572-9141 (online) |
Volume:
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68 |
Issue:
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3 |
Year:
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2018 |
Pages:
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711-721 |
Summary lang:
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English |
. |
Category:
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math |
. |
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. (English) |
Keyword:
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3-Leibniz algebras |
Keyword:
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Rota-Baxter 3-Lie algebras |
Keyword:
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3-Lie 2-algebras |
MSC:
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17B99 |
MSC:
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55U15 |
idZBL:
|
Zbl 06986967 |
idMR:
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MR3851886 |
DOI:
|
10.21136/CMJ.2018.0627-16 |
. |
Date available:
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2018-08-09T13:12:05Z |
Last updated:
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2020-10-05 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/147363 |
. |
Reference:
|
[1] Baez, J. C., Crans, A. S.: Higher-dimensional algebra. VI. Lie 2-algebras.Theory Appl. Categ. 12 (2004), 492-538. Zbl 1057.10711, MR 2068522 |
Reference:
|
[2] Baez, J. C., Rogers, C. L.: Categorified symplectic geometry and the string Lie 2-algebra.Homology Homotopy Appl. 12 (2010), 221-236. Zbl 1277.70031, MR 2638872, 10.4310/HHA.2010.v12.n1.a12 |
Reference:
|
[3] Bai, R., Guo, L., Li, J., Wu, Y.: Rota-Baxter 3-Lie algebras.J. Math. Phys. 54 (2013), 063504, 14 pages. Zbl 1366.17003, MR 3112546, 10.1063/1.4808053 |
Reference:
|
[4] Casas, J. M.: Trialgebras and Leibniz 3-algebras.Bol. Soc. Mat. Mex., III. Ser. 12 (2006), 165-178. Zbl 1151.17001, MR 2292981 |
Reference:
|
[5] Casas, J. M., Loday, J.-L., Pirashvili, T.: Leibniz $n$-algebras.Forum Math. 14 (2002), 189-207. Zbl 1037.17002, MR 1880911, 10.1515/form.2002.009 |
Reference:
|
[6] Chen, S., Sheng, Y., Zheng, Z.: Non-abelian extensions of Lie 2-algebras.Sci. China, Math. 55 (2012), 1655-1668. Zbl 1280.17026, MR 2955249, 10.1007/s11425-012-4398-7 |
Reference:
|
[7] Lang, H., Liu, Z.: Crossed modules for Lie 2-algebras.Appl. Categ. Struct. 24 (2016), 53-78. Zbl 06541802, MR 3448428, 10.1007/s10485-015-9389-8 |
Reference:
|
[8] Liu, Z., Sheng, Y., Zhang, T.: Deformations of Lie 2-algebras.J. Geom. Phys. 86 (2014), 66-80. Zbl 1362.17032, MR 3282312, 10.1016/j.geomphys.2014.07.020 |
Reference:
|
[9] Loday, J.-L., Frabetti, A., Chapoton, F., Goichot, F., eds.: Dialgebras and Related Operads.Lecture Notes in Mathematics 1763, Springer, Berlin (2001). Zbl 0970.00010, MR 1864390, 10.1007/b80864 |
Reference:
|
[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. Zbl 1065.18007, MR 2066507, 10.1090/conm/346/06296 |
Reference:
|
[11] Ni, J., Wang, Y., Hou, D.: Super $\scr O $-operators of Jordan superalgebras and super Jordan Yang-Baxter equations.Front. Math. China 9 (2014), 585-599. Zbl 1333.17025, MR 3195837, 10.1007/s11464-014-0339-9 |
Reference:
|
[12] Noohi, B.: Integrating morphisms of Lie 2-algebras.Compos. Math. 149 (2013), 264-294. Zbl 1315.22023, MR 3020309, 10.1112/S0010437X1200067X |
Reference:
|
[13] Sheng, Y., Chen, D.: Hom-Lie 2-algebras.J. Algebra 376 (2013), 174-195. Zbl 1281.17034, MR 3003723, 10.1016/j.jalgebra.2012.11.032 |
Reference:
|
[14] Sheng, Y., Liu, Z.: From Leibniz algebras to Lie 2-algebras.Algebr. Represent. Theory 19 (2016), 1-5. Zbl 06563849, MR 3465885, 10.1007/s10468-015-9556-5 |
Reference:
|
[15] Sheng, Y., Liu, Z., Zhu, C.: Omni-Lie 2-algebras and their Dirac structures.J. Geom. Phys. 61 (2011), 560-575. Zbl 1242.17026, MR 2746137, 10.1016/j.geomphys.2010.11.005 |
Reference:
|
[16] Sheng, Y., Zhu, C.: Integration of Lie 2-algebras and their morphisms.Lett. Math. Phys. 102 (2012), 223-244. Zbl 1335.17008, MR 2984165, 10.1007/s11005-012-0578-1 |
Reference:
|
[17] Sheng, Y., Zhu, C.: Integration of semidirect product Lie 2-algebras.Int. J. Geom. Methods Mod. Phys. 9 (2012), 1250043, 31 pages. Zbl 1277.17012, MR 2948862, 10.1142/S0219887812500430 |
Reference:
|
[18] Zhou, Y., Li, Y., Sheng, Y.: 3-Lie$_{\infty}$-algebras and 3-Lie 2-algebras.J. Algebra Appl. 16 (2017), Article ID 1750171, 20 pages. Zbl 06745725, MR 3661638, 10.1142/S0219498817501717 |
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