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arXiv · 2210.12550

Segre products and Segre morphisms in a class of Yang-Baxter algebras

Tatiana Gateva-Ivanova
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Abstract

Let $(X,r_X)$ and $(Y,r_Y)$ be finite nondegenerate involutive set-theoretic solutions of the Yang-Baxter equation, and let $A_X = A(\textbf{k}, X, r_X)$ and $A_Y= A(\textbf{k}, Y, r_Y)$ be their quadratic Yang-Baxter algebras over a field $\textbf{k}.$ We find an explicit presentation of the Segre product $A_X\circ A_Y$ in terms of one-generators and quadratic relations. We introduce analogues of Segre maps in the class of Yang-Baxter algebras and find their images and their kernels. The results agree with their classical analogues in the commutative case.

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Tatiana Gateva-Ivanova. 2022-10-22. Segre products and Segre morphisms in a class of Yang-Baxter algebras. https://doi.org/10.1007/s11005-023-01657-z

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