%0 Journal Article %T Construction of graded differential algebra with ternary differential %A Nadezda Bazunova %J Mathematics %D 2005 %I arXiv %R 10.2991/jnmp.2006.13.s.3 %X In this article, we describe the construction of graded $q$-differential algebra with ternary differential satisfying the property $d^3=0$ and the $q$-Leibniz rule. Our starting point is coordinate first order differential calculus on some complex algebra and the corresponding bimodule of second order differentials. %U http://arxiv.org/abs/math-ph/0509015v1