A bijective map r : X −→ X, where X = {x1, · · · , xn} is a finite set, is called a set-theoretic solution of the Yang-Baxter equation (YBE) if the braid relation r12r23r12 = r23r12r23 holds in X. A… (More)

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

The paper considers computer algebra in a non-commutative setting. So far, such investigations have been centred on the use of algorithms for equality and of universal properties of algebras. Here,… (More)

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 involutive square-free… (More)

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 level two can be put in… (More)

We show the intimate connection between various mathematical notions that are currently under active investigation: a class of Garside monoids, with a “nice” Garside element, certain monoids S with… (More)

We consider algebras over a field K defined by a presentation K〈x1, . . . , xn : R〉, where R consists of ( n 2 ) square-free relations of the form xixj = xkxl with every monomial xixj , i 6= j,… (More)

Tatiana Gateva-Ivanova, American University in Bulgaria Noncommutative Gr obner Bases in Skew-polynomial Rings We study a class of graded standard nitely presented quadratic algebras A over a xed… (More)