Braces were introduced by Rump to study non-degenerate involutive set-theoretic solutions
of the Yang–Baxter equation. We generalize Rump's braces to the non-commutative setting …

0. Introduction. The quantum Yang-Baxter equation (QYBE) is one of the basic equations in
mathematical physics that lies in the foundation of the theory of quantum groups. This …

Non-degenerate cycle sets are equivalent to non-degenerate unitary set-theoretical
solutions of the quantum Yang–Baxter equation. We embed such cycle sets into generalized …

Braces are generalizations of radical rings, introduced by Rump to study involutive non-
degenerate set-theoretical solutions of the Yang–Baxter equation (YBE). Skew braces were …

Several aspects of relations between braces and non-degenerate involutive set-theoretic
solutions of the Yang–Baxter equation are discussed and many consequences are derived …

It is known that every skew-polynomial ring with generating set X and binomial relations in
the sense of Gateva-Ivanova (Trans. Amer. Math. Soc. 343 (1994) 203) is an Artin-Schelter …

A natural, but slowly emerging program. In his PhD thesis prepared under the supervision of
Graham Higman and defended in 1965 [123], and in the article that followed [124], FA …

We involve simultaneously the theory of braided groups and the theory of braces to study set-
theoretic solutions of the Yang–Baxter equation (YBE). We show the intimate relation …

Our primary focus is on the theory of skew braces, specifically exploring their connection
with combinatorial solutions to the Yang–Baxter equation. Skew braces have recently …

Accepted Manuscript Page 1 Agata Smoktunowicz On Engel groups, nilpotent groups, rings,
braces and the Yang-Baxter equation Transactions of the American Mathematical Society DOI …