Basics of Ternary Algebras and their underlying Nambu Brackets

Branes, Strings, and Odd Quantum Nambu Brackets

The dynamics of topological open branes is controlled by Nambu Brackets. Thus, they might be quantized through the consistent quantization of the underlying Nambu brackets, including odd ones: these are reachable systematically from even brackets, whose more tractable properties have been detailed before. The classical motion of topological open membranes is controlled by Nambu Brackets, the mu...

A Survey on Nambu–Poisson Brackets

The paper provides a survey of known results on geometric aspects related to Nambu-Poisson brackets.

Non-antisymmetric versions of Nambu-Poisson and Lie algebroid brackets

We show that we can skip the skew-symmetry assumption in the definition of Nambu-Poisson brackets. In other words, a n-ary bracket on the algebra of smooth functions which satisfies the Leibniz rule and a n-ary version of the Jacobi identity must be skew-symmetric. A similar result holds for a non-antisymmetric version of Lie algebroids.

Dynamics of generalized Poisson and Nambu–Poisson brackets

Branes, Quantum Nambu Brackets, and the Hydrogen Atom

The Nambu Bracket quantization of the Hydrogen atom is worked out as an illustration of the general method. The dynamics of topological open branes is controlled classically by Nambu Brackets. Such branes then may be quantized through the consistent quantization of the underlying Nambu brackets: properly defined, the Quantum Nambu Brackets comprise an associative structure, although the naive d...