Research introduces Np-graded biracks and their isotopes, revealing implications for Yang-Baxter 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.
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Yu et al. (2026) studied this question.
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