Isotopes of Biracks and Zhang Twists of Algebras

In this paper, we introduce the notion of an Np-graded birack and construct its isotope. Every involutive Np-graded birack gives rise to an Np-graded Yang-Baxter algebra. We study the relation between isotopes of involutive Np-graded biracks and Zhang twists of Np-graded Yang-Baxter algebras. As an example, Yang-Baxter algebras determined by distributive solutions are proved to be Zhang twists of polynomial algebras.