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

Abstract

Let $(X,r_X)$ and $(Y,r_Y)$ be finite nondegenerate involutive set-theoretic solutions of the Yang-Baxter equation, and let $A_X=A(\text{k},X,r_X)$ and $A_Y=A(\text{k},Y,r_Y)$ be their quadratic Yang-Baxter algebras over a field $\text{k}.$ 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.

21 pages. arXiv admin note: substantial text overlap with arXiv:2204.08850

References in corpus (3)

• A combinatorial approach to noninvolutive set-theoretic solutions of the Yang-Baxter equation
• Segre products and Segre morphisms in a class of Yang-Baxter algebras
• Veronese and Segre morphisms between non-commutative projective spaces

Cited by in corpus (1)

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