Non-coordinate case of graded differential algebra with ternary differential

Abstract

In this article, we generalize a construction of graded q-differential algebra with ternary differential satisfying the property d3 = 0 and q-Leibniz rule on the non-coordinate case, that is on the case where the differentials of generators of underlying algebra do not coincide with generators of bimodule of first order forms. Our starting point is the coordinate first order differential calculus on associative complex algebra A with n generators and the bimodule of second order differentials.