Geodesic
Hopf structure in Nambu–Lie $n$-algebras
Teoretičeskaâ i matematičeskaâ fizika, Tome 114 (1998) no. 1, pp. 87-93 
R. Muradian; A. E. Santana. Hopf structure in Nambu–Lie $n$-algebras. Teoretičeskaâ i matematičeskaâ fizika, Tome 114 (1998) no. 1, pp. 87-93. http://geodesic.mathdoc.fr/item/TMF_1998_114_1_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We define and study the Hopf structures in the ternary (and $n$-ary) Nambu–Lie algebra. The fundamental concepts of 3-coalgebra, 3-bialgebra, and Hopf 3-algebra are introduced. Some examples of the Hopf structures are analyzed.

[1] Y. Nambu, Phys. Rev. D, 7 (1973), 2405–2412 | DOI | MR | Zbl

[2] F. Bayen, M. Flato, Phys. Rev. D, 11 (1975), 3049–3052 | DOI | MR

[3] G. J. Ruggeri, Lett. Nuovo Cim., 17 (1976), 169–171 | DOI | MR

[4] F. Bayen, M. Flato, C. Fronsdal, A. Lichnerovicz, D. Sternheimer, Ann. Phys., 110 (1978), 67–110, 111–151 | MR

[5] G. Dito, M. Flato, D. Sternheimer, L. Takhtajan, Commun. Math. Phys., 183 (1997), 1–22 | DOI | MR | Zbl

[6] G. Dito, M. Flato, Lett. Math. Phys., 39 (1997), 107–125 | DOI | MR | Zbl

[7] L. A. Takhtajan, Commun. Math. Phys., 160 (1994), 295–315 | DOI | MR | Zbl

[8] L. A. Takhtadzhyan, Algebra i analiz, 6:2 (1994), 262–272 | MR | Zbl

[9] R. Chatterjee, L. Takhtajan, Lett. Math. Phys., 37 (1996), 475–482 | DOI | MR | Zbl

[10] H. Q. Plácido, R. Bunchaft, A. E. Santana, Hadronic J., 15 (1992), 225–238 | MR | Zbl

[11] D. Sahoo, M. C. Valsakumar, Mod. Phys. Lett., 9 (1994), 2727–2732 | DOI | MR | Zbl

[12] P. Gautheron, Lett. Math. Phys., 37 (1996), 103–116 | DOI | MR | Zbl

[13] A. E. Santana, T. Kopf, F. C. Khanna, “Hopf algebras, Lie symmetries and thermal field theories”, Proceedings of Lake Louise International Conference on High Energy Physics, Canada, 1997 (to appear) | MR

[14] J. Madore, Introduction to Noncommutative Geometry and its Applications, Cambridge University Press, Cambridge, 1995 | MR | Zbl