Ternutator Identities

Abstract

The ternary commutator or ternutator, defined as the alternating sum of the product of three operators, has recently drawn much attention as an interesting structure generalising the commutator. The ternutator satisfies cubic identities analogous to the quadratic Jacobi identity for the commutator. We present various forms of these identities and discuss the possibility of using them to define ternary algebras.

12 pages, citation added

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Cited by in corpus (6)

• n-ary algebras: a review with applications
• Multi-operator brackets acting thrice
• The partially alternating ternary sum in an associative dialgebra
• $W_{1+\infty }$ constraints for the hermitian one-matrix model
• Higher identities for the ternary commutator
• Necessary conditions for Ternary Algebras