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Abstract
Braces are generalizations of radical rings, introduced by Rump to study involutive nondegenerate settheoretical solutions of the YangBaxter equation (YBE). Skew braces were also recently introduced as a tool to study not necessarily involutive solutions. Roughly speaking, skew braces provide grouptheoretical and ringtheoretical methods to understand solutions of the YBE. It turns out that skew braces appear in many different contexts, such as nearrings, matched pairs of groups, triply factorized groups, bijective 1cocycles and HopfGalois extensions. These connections and some of their consequences are explored in this paper. We produce several new families of solutions related in many different ways with rings, nearrings and groups. We also study the solutions of the YBE that skew braces naturally produce. We prove, for example, that the order of the canonical solution associated with a finite skew brace is even: it is two times the exponent of the additive group modulo its center.
Original language  English 

Pages (fromto)  4786 
Number of pages  37 
Journal  Journal of Combinatorial Algebra 
Volume  2 
Issue number  1 
Early online date  8 Feb 2018 
DOIs  
Publication status  Published  Feb 2018 
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Dive into the research topics of 'On Skew Braces (with an appendix by N. Byott and L. Vendramin)'. Together they form a unique fingerprint.Projects
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Agata Smoktunowicz
 School of Mathematics  Personal Chair in Algebra
Person: Academic: Research Active