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 …

This book is addressed to graduate students and researchers in the fields of mathematics
and physics who are interested in mathematical and theoretical physics, differential …

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 …

1. Introduction. Lie bialgebras arise as infinitesimal invariants of Poisson Lie groups. A Lie
bialgebra is a Lie algebra I with a Lie algebra structure on the dual g* which is compatible …

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 …

In this article we shall give an account of certain developments in knot theory which followed
upon the discovery of the Jones polynomial [Jo3] in 1984. The focus of our account will be …

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 …

In [D], Drinfel'd raised the question of finding set-theoretical solutions of the Yang-Baxter
equation. Specifically, we consider a set S and an invertible map R: S× S→ S× S. We think of …

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 …