Talk:Ternary commutator

What are these?

 * $$[a,b,c] = abc-acb-bac+bca+cab-cba. \, $$

Are $$a,b,c$$ vectors are scalars or matrices or what? Michael Hardy (talk) 15:52, 28 July 2012 (UTC)


 * They're most likely to be matrices, but I suppose the setting could be any abelian group with a given ternary "product" operation. For the purposes of Bremner (1998), the setting is a triple system, i.e. a vector space with a trilinear map. Other authors may restrict their attention to associative algebras. Melchoir (talk) 19:04, 28 July 2012 (UTC)