Ternary commutator
In today's world, Ternary commutator has gained great relevance in different areas of daily life. From its impact on society to its influence on the global economy, Ternary commutator has become a topic of discussion and debate that leaves no one indifferent. Throughout history, Ternary commutator has played a fundamental role in the evolution and development of humanity, marking important milestones and generating significant changes. In this article, we will explore in detail the impact of Ternary commutator in various areas, analyzing its relevance and contribution to the way we perceive and cope with the world today.
In mathematical physics, the ternary commutator is an additional ternary operation on a triple system defined by
Also called the ternutator or alternating ternary sum, it is a special case of the n-commutator for n = 3, whereas the 2-commutator is the ordinary commutator.
Properties
- When one or more of a, b, c is equal to 0, is also 0. This statement makes 0 the absorbing element of the ternary commutator.
- The same happens when a = b = c.
Further reading
- Bremner, Murray R. (15 August 1998), "Identities for the Ternary Commutator", Journal of Algebra, 206 (2): 615–623, doi:10.1006/jabr.1998.7433
- Bremner, Murray R.; Ortega, Juana Sánchez (25 October 2010), "The partially alternating ternary sum in an associative dialgebra", Journal of Physics A: Mathematical and Theoretical, 43 (56) 455215, arXiv:1008.2721, Bibcode:2010JPhA...43S5215B, doi:10.1088/1751-8113/43/45/455215, S2CID 6636902
- Bremner, Murray R.; Peresi, Luiz A. (1 April 2006), "Ternary analogues of Lie and Malcev algebras", Linear Algebra and Its Applications, 414 (1): 1–18, doi:10.1016/j.laa.2005.09.004
- Bremner, Murray R.; Peresi, Luiz A. (26 July 2012), "Higher identities for the ternary commutator", Journal of Physics A: Mathematical and General, 45 (50) 505201, arXiv:1207.6312, Bibcode:2012JPhA...45X5201B, doi:10.1088/1751-8113/45/50/505201, S2CID 17037773
- Devchand, Chandrashekar; Fairlie, David; Nuyts, Jean; Weingart, Gregor (6 November 2009), "Ternutator identities", Journal of Physics A: Mathematical and Theoretical, 42 (47) 475209, arXiv:0908.1738, Bibcode:2009JPhA...42U5209D, doi:10.1088/1751-8113/42/47/475209, S2CID 17246666
- Nambu, Yoichiro (1973), "Generalized Hamiltonian Dynamics", Physical Review D, 7 (8): 2405–2412, Bibcode:1973PhRvD...7.2405N, doi:10.1103/PhysRevD.7.2405
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