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, [a, b, c] 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.; 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