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arXiv · 2512.03384

Isotopes of biracks and Zhang twists of algebras

Xiaolan Yu·Yanfei Zhang
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Abstract

In this paper, we introduce the notion of an $\mathbb{N}^p$-graded birack and construct its isotope. Every involutive $\mathbb{N}^p$-graded birack gives rise to an $\mathbb{N}^p$-graded Yang-Baxter algebra. We study the relation between isotopes of involutive $\mathbb{N}^p$-graded biracks and Zhang twists of $\mathbb{N}^p$-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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Xiaolan Yu, Yanfei Zhang. 2025-12-03. Isotopes of biracks and Zhang twists of algebras. https://arxiv.org/abs/2512.03384

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