×

On non-abelian extensions of 3-Lie algebras. (English) Zbl 1402.17010

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.

MSC:

17A40 Ternary compositions
17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
17A32 Leibniz algebras
PDFBibTeX XMLCite
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.