WebThe ideal extension of skew left braces is a generalization to the non-abelian case of the extension of left braces provided by Bachiller in [D. Bachiller, Extensions, matched products, and simple ... WebJun 8, 2024 · As an illustration, we give a simple proof of a recent theorem of Smoktunowicz on braces with nilpotent adjoint group, and a classification of braces with …

Extensions of linear cycle sets and cohomology SpringerLink

WebJul 27, 2024 · We investigate the matched product of solutions associated with right and left shelves. First, we prove that the requirements to provide the matched product of solutions that come from shelves can be simplified. Then we give conditions for left non-degeneracy of the matched product. Later, we compute the structure shelf of the matched product of … WebGiven a skew left brace B, a method is given to construct all the non-degenerate set-theoretic solutions ( X, r) of the Yang–Baxter equation such that the associated permutation group 𝒢 ( X, r) is isomorphic, as a skew left brace, to B. This method depends entirely on the brace structure of B. the corner series

Extensions, matched products, and simple braces - CORE …

WebBachiller, Extensions, matched products and simple braces, J. Pure Appl. Algebra 222 (2024) 1670–1691. ... Vendramin, Extensions of set-theoretic solutions of the … WebDec 20, 2024 · In this article, we give a description of the split exact sequences of left skew braces. We define a free action of the second cohomology group of a left skew brace H by Ann(I) on Extα(H, I) and show that this action becomes transitive if I is a trivial skew brace. We also generalize the Well’s type exact sequence for extensions by the trivial skew … WebExtensions, matched products, and simple braces @article{Bachiller2015ExtensionsMP, title={Extensions, matched products, and simple braces}, author={David Bachiller}, journal={Journal of Pure and Applied Algebra}, year={2015} } D. Bachiller; Published 26 November 2015; Mathematics; Journal of Pure and Applied Algebra the corner series netflix