Year: 2023
Type: article
Abstract: Let $$(X,r_X)$$ ( X , r X ) and $$(Y,r_Y)$$ ( Y , r Y ) be finite nondegenerate involutive set-theoretic solutions of the Yang–Baxter equation, and let $$A_X = \mathcal {A}({{\textbf {k}}}, X, r_X)$$ A X = A ( k , X , r X ) and $$A_Y= \mathcal {A}({{\textbf {k}}}, Y, r_Y)$$ A Y = A ( k , Y , r Y ) be their quadratic Yang–Baxter algebras over a field $${{\textbf {k}}}$$ k . We find an explicit presentation of the Segre product $$A_X\circ A_Y$$ A X ∘ 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.
Source: Letters in Mathematical Physics
Author: Tatiana Gateva-Ivanova
Language: Latvian
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,690
Awards: G2025473196, G3738815112
OpenAlex ID: W4327761965