Necessary conditions for Ternary Algebras

Details Necessary conditions for Ternary Algebras Necessary conditions for Ternary Algebras

2010-07-22

arxiv.org/abs/1007.3871v1

J.Phys.A43:465202,2010

Physics

High Energy Physics

High Energy Physics - Theory

10 pages

Scientific paper

10.1088/1751-8113/43/46/465202

Ternary algebras, constructed from ternary commutators, or as we call them, ternutators, defined as the alternating sum of products of three operators, have been shown to satisfy cubic identities as necessary conditions for their existence. Here we examine the situation where we permit identities not solely constructed from ternutators or nested ternutators and we find that in general, these impose additional restrictions; for example, the anti-commutators or commutators of the operators must obey some linear relations among themselves.

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