Extensions of Yang-Baxter sets

Dmitry V. Talalaev; Valeriy G. Bardakov

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Extensions of Yang-Baxter sets

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arxiv 2206.09629 v1 pith:O65HY5SP submitted 2022-06-20 math.QA math.GR

Valeriy G. Bardakov , Dmitry V. Talalaev This is my paper · ORCID

classification math.QAmath.GR

keywords yang-baxterequationextensionsnotionsolutionsaspectsbraidbraided

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The paper extends the notion of braided set and its close relative - the Yang-Baxter set - to the category of vector spaces and explore structure aspects of such a notion as morphisms and extensions. In this way we describe a family of solutions for the Yang-Baxter equation on the product of B and C if given B and C correspond to two linear (set-theoretic) solutions of the Yang-Baxter equation. One of the key observation is the relation of this question with the virtual pure braid group.

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