Song, Li-Na; Makhlouf, Abdenacer; Tang, Rong On non-abelian extensions of 3-Lie algebras. (English) Zbl 1402.17010 Commun. Theor. Phys. 69, No. 4, 347-356 (2018). Summary: In this paper, we study non-abelian extensions of 3-Lie algebras through Maurer-Cartan elements. We show that there is a one-to-one correspondence between isomorphism classes of non-abelian extensions of 3-Lie algebras and equivalence classes of Maurer-Cartan elements in a DGLA. The structure of the Leibniz algebra on the space of fundamental objects is also analyzed. Cited in 4 Documents MSC: 17A40 Ternary compositions 17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.) 17A32 Leibniz algebras Keywords:3-Lie algebras; Leibniz algebra; non-abelian extension; Maurer-Cartan element PDFBibTeX XMLCite \textit{L.-N. Song} et al., Commun. Theor. Phys. 69, No. 4, 347--356 (2018; Zbl 1402.17010) Full Text: DOI arXiv References: [1] Filippov, V. T., Sib. Mat. Zh., 26, 126, (1985) [2] Nambu, Y., Phys. Rev. D, 7, 2405, (1973) [3] Takhtajan, L., Commun. Math. Phys., 160, 295, (1994) [4] Gautheron, P., Lett. Math. Phys., 37, 103, (1996) [5] Basu, A.; Harvey, J. A., Nucl. Phys. B, 713, 136, (2005) [6] Bagger, J.; Lambert, N., Phys. Rev. D, 77, (2008) [7] Bagger, J.; Lambert, N., Phys. Rev. D, 79, (2009) [8] Gomis, J.; Rodriguez-Gómez, D.; Van Raamsdonk, M.; Verlinde, H., J. High Energy Phys., 8, 094, (2008) [9] Ho, P. M.; Matsuo, Y., J. High Energy Phys., 06, 105, (2008) [10] Ho, P. M.; Hou, R.; Matsuo, Y., J. High Energy Phys., 6, 020, (2008) [11] Papadopoulos, G., J. High Energy Phys., 5, 054, (2008) [12] Kasymov, Sh. M., Algebra i Logika, 26, 277, (1987) [13] Daletskii, Y.; Takhtajan, L., Lett. Math. Phys., 39, 127, (1997) [14] Figueroa-O’Farrill, J., J. Math. Phys., 50, (2009) [15] de Azcárraga, J. A.; Izquierdo, J. M., J. Phys. Conf. Ser., 175, (2009) [16] Takhtajan, L., St. Petersburg Math. J., 6, 429, (1995) [17] Bai, R.; Bai, C.; Wang, J., J. Math. Phys., 51, (2010) [18] Bai, R.; Song, G.; Zhang, Y., Front. Math. China, 6, 581, (2011) [19] Rotkiewicz, M., Extracta Math., 20, 219, (2005) [20] de Azcárraga, J. A.; Izquierdo, J. M., J. Phys. A: Math. Theor., 43, (2010) · Zbl 1202.81187 [21] Makhlouf, A.; Gueye, C. T.; Molina, M. S., Proceedings in Mathematics & Statistics, 160, Chapter 4 in Non Associative & Non Commutative Algebra and Operator Theory, (2016), Springer: Springer, Mulhouse [22] Liu, J.; Makhlouf, A.; Sheng, Y., Algebr Represent Theor., 20, 1415, (2017) [23] Fregier, Y., J. Algebra, 398, 243, (2014) [24] Loday, J. L., Enseign. Math., 39, 269, (1993) [25] Loday, J. L.; Pirashvili, T., Math. Ann., 296, 139, (1993) [26] Liu, J.; Sheng, Y.; Wang, Q., Commun. Algebra., 46, 574, (2018) [27] Dolgushev, V. A., Stable Formality Quasi-Isomorphisms for Hochschild Cochains This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.