Brackets of Nambu, on d-polynomials and on canonical lists of variables

In this paper we define d-polynomials which are generalized polynomials with noncommuting coefficients inserted between the variables. We show that some d-polynomials can be used as an extension of the brackets of Nambu. As a result, we obtain that n mutually commutative Heisenberg pairs of canonical variables, sigma-Pauli matrices, and lambda-Gell-Mann matrices can be considered in a unified way as canonical lists of variables