American University in Bulgaria

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20022025

most citedA combinatorial approach to the set-theoretic solutions of the Yang-Baxter equation

85 citations

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8 papers · 1 filter

math.QA2022★ 3 cited

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

Tatiana Gateva-Ivanova

Let $(X, r_{X})$ and $(Y, r_{Y})$ be finite nondegenerate involutive set-theoretic solutions of the Yang-Baxter equation, and let $A_{X} = A (k, X, r_{X})$ and $A_Y= A(\textbf{k}, Y,…

math.QA2020★ 1 cited

Veronese and Segre morphisms between non-commutative projective spaces

Francesca Arici, Francesco Galuppi, Tatiana Gateva-Ivanova

We study Veronese and Segre morphisms between non-commutative projective spaces. We compute finite reduced Gröbner bases for their kernels, and we compare them with their analogues…

math.QA2018★ 13 cited

A combinatorial approach to noninvolutive set-theoretic solutions of the Yang-Baxter equation

Tatiana Gateva-Ivanova

We study noninvolutive set-theoretic solutions $(X, r)$ of the Yang-Baxter equations in terms of the properties of the canonically associated algebraic objects-the braided monoid $S…

math.QA2009★ 3 cited

Multipermutation solutions of the Yang--Baxter equation

Tatiana Gateva-Ivanova, Peter Cameron

Set-theoretic solutions of the Yang--Baxter equation form a meeting-ground of mathematical physics, algebra and combinatorics. Such a solution consists of a set $X$ and a function…

math.QA2008★ 6 cited

Quantum spaces associated to multipermutation solutions of level two

Tatiana Gateva-Ivanova, Shahn Majid

We study finite set-theoretic solutions $(X, r)$ of the Yang-Baxter equation of square-free multipermutation type. We show that each such solution over $\C$ with multipermutation le…

math.QA2007★ 1 cited

Set theoretic solutions of the Yang-Baxter equation, graphs and computations

Tatiana Gateva-Ivanova, Shahn Majid

We extend our recent work on set-theoretic solutions of the Yang-Baxter or braid relations with new results about their automorphism groups, strong twisted unions of solutions and…

math.QA2005★ 3 cited

Matched pairs approach to set-theoretic solutions of the Yang-Baxter equation

Tatiana Gateva-Ivanova, Shahn Majid

We study set-theoretic solutions $(X, r)$ of the Yang-Baxter equations on a set $X$ in terms of the induced left and right actions of $X$ on itself. We give a characterization of in…

math.QA2004★ 85 cited

A combinatorial approach to the set-theoretic solutions of the Yang-Baxter equation

Tatiana Gateva-Ivanova

A bijective map $r : X^{2} ⟶ X^{2}$ , where $X = {x_{1}, ..., x_{n}}$ is a finite set, is called a \emph{set-theoretic solution of the Yang-Baxter equation} (YBE) if the bra…