70
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Deformations and cohomologies of embedding tensors on 3-Lie algebras

, , &
Pages 4622-4639 | Received 04 Dec 2022, Accepted 08 May 2023, Published online: 27 May 2023

References

  • Aguiar, M. (2000). Pre-Poisson algebras. Lett. Math. Phys. 54:263–277. DOI: 10.1023/A:1010818119040.
  • Bai, C., Guo, L., Sheng, Y. (2019). Bialgebras, the classical Yang-Baxter equation and Manin triples for 3-Lie algebras. Adv. Theor. Math. Phys. 23:27–74. DOI: 10.4310/ATMP.2019.v23.n1.a2.
  • Bai, R., Guo, L., Li, J., Wu, Y. (2013). Rota-Baxter 3-Lie algebras. J. Math. Phys. 54:063504, 14 pp. DOI: 10.1063/1.4808053.
  • Bergshoeff, E. A., de Roo, M., Hohm, O. (2008). Multiple M2-branes and the embedding tensor. Class. Quantum Gravity 25:142001, 10 pp. DOI: 10.1088/0264-9381/25/14/142001.
  • Casas, J. M., Loday, J. -L., Pirashvili, T. (2002). Leibniz n-algebras. Forum Math. 14:189–207.
  • de Azcárraga, J. A., Izquierdo, J. M. (2010). n-ary algebras: a review with applications. J. Phys. A: Math. Theor. 43:293001. DOI: 10.1088/1751-8113/43/29/293001.
  • de Medeiros, P., Figueroa-O’Farrill, J., Méndez-Escobar, E., Ritter, P. (2009). On the Lie-algebraic origin of metric 3-algebras. Commun. Math. Phys. 290:871–902.
  • Figueroa-O’Farrill, J. (2009). Deformations of 3-algebras. J. Math. Phys. 50:113514, 27 pp.
  • Filippov, V. T. (1985). n-Lie algebras. Sibirsk. Mat. Zh. 26:126–140.
  • Getzler, E. (2009). Lie theory for nilpotent L∞ -algebras. Ann. Math. (2) 170:271–301.
  • Goncharov, M. E., Kolesnikov, P. S. (2018). Simple finite-dimensional double algebras. J. Algebra 500:425–438. DOI: 10.1016/j.jalgebra.2017.04.020.
  • Hanlon, P., Wachs, M. (1995). On Lie k-algebras. Adv. Math. 113:206–236. DOI: 10.1006/aima.1995.1038.
  • Kasymov, Sh. M. (1987). On a theory of n-Lie algebras. Algebra i Logika 26:277–297.
  • Kotov, A., Strobl, T. (2020). The embedding tensor, Leibniz-Loday algebras, and their higher Gauge theories. Commun. Math. Phys. 376:235–258. DOI: 10.1007/s00220-019-03569-3.
  • Lada, T., Stasheff, J. (1993). Introduction to SH Lie algebras for physicists. Int. J. Theor. Phys. 32:1087–1103. DOI: 10.1007/BF00671791.
  • Makhlouf, A. (2016). On deformations of n-Lie algebras. In: Gueye, C. T., Molina, M. S., eds. Non-associative and Non-commutative Algebra and Operator Theory. Springer Proceedings in Mathematics & Statistics, Vol. 160. Cham: Springer, pp. 55–81.
  • Masahito, Y. (2008). Octonions, G2 and generalized Lie 3-algebras. Phys. Lett. B 670:215–219.
  • Nambu, Y. (1973). Generalized Hamiltonian dynamics. Phys. Rev. D 7:2405–2412. DOI: 10.1103/PhysRevD.7.2405.
  • Nicolai, H., Samtleben, H. (2001). Maximal gauged supergravity in three dimensions. Phys. Rev. Lett. 86:1686–1689. DOI: 10.1103/PhysRevLett.86.1686.
  • Pei, J., Bai, C., Guo, L., Ni, X. (2020). Replicating of binary operads, Koszul duality, Manin products and average operators. New Trends Algebras Comb. 317–353.
  • Pei, J., Guo, L. (2015). Averaging algebras, Schröder numbers, rooted trees and operads. J. Algebraic Combin. 42:73–109. DOI: 10.1007/s10801-014-0574-x.
  • Rotkiewicz, M. (2005). Cohomology ring of n-Lie algebras. Extracta Math. 20:219–232.
  • Sheng, Y., Tang, R., Zhu, C. (2021). The controlling L∞ -algebra, cohomology and homotopy of embedding tensors and Lie-Leibniz triples. Commun. Math. Phys. 386:269–304.
  • Sheng, Y., Tang, R. (2018). Symplectic, product and complex structures on 3-Lie algebras. J. Algebra 508:256–300. DOI: 10.1016/j.jalgebra.2018.05.005.
  • Schlessinger, M., Stasheff, J. (1985). The Lie algebra structure of tangent cohomology and deformation theory.J. Pure Appl. Algebra 38:313–322. DOI: 10.1016/0022-4049(85)90019-2.
  • Stasheff, J. (1992). Differential graded Lie algebras, quasi-Hopf algebras and higher homotopy algebras. In: Quantum Groups (Leningrad, 1990), Lecture Notes in Mathematics, Vol. 1510. Berlin: Springer, pp. 120–137.
  • Takhtajan, L. A. (1995). Higher order analog of Chevalley-Eilenberg complex and deformation theory of n-gebras. St. Petersburg Math. J. 6:429–438.
  • Tang, R., Hou, S., Sheng, Y. (2021). Lie 3-algebras and deformations of relative Rota-Baxter operators on 3-Lie algebras. J. Algebra 567:37–62. DOI: 10.1016/j.jalgebra.2020.09.017.
  • Voronov, Th. (2005). Higher derived brackets and homotopy algebras. J. Pure Appl. Algebra 202:133–153. DOI: 10.1016/j.jpaa.2005.01.010.
  • Zheng, S., Guo, L., Rosenkranz, M. (2015). Rota-Baxter operators on the polynomial algebra, integration, and averaging operators. Pac. J. Math. 275:481–507. DOI: 10.2140/pjm.2015.275.481.
  • Zhou, Y., Li, Y., Sheng, Y. (2017). 3-Lie∞ -algebras and 3-Lie 2-algebras. J. Algebra Appl. 16:1750171, 20 pp.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.