Representation theory of skew braces
type: Item
instance of: scholarly article
title: Representation theory of skew braces
author: Yuta Kozakai
author: Cindy (Sin Yi) Tsang
published in: International Journal of Group Theory
publication date: 2024-11-28T00:00:00Z
review text: A skew (left) brace is a set \(A=(A,\ast,\circ)\) equipped with two group operations \(\ast\) and \(\circ\) such that the so-called brace relation \(a \circ (b \ast c) = (a \circ b) \ast a^{-1} \ast (a \circ c)\) holds for all \(a, b, c \in A\). A brace is a skew brace with \((A, \ast)\) abelian. According to \textit{T. Letourmy} and \textit{L. Vendramin} [J. Algebra 644, 609--654 (2024; Zbl 07804819)], a representation of a skew brace is a pair of representations on the same vector space, one for \((A, \ast)\) and the other for \((A, \circ)\), that satisfies a certain compatibility condition.\N\NIn the paper under review the authors, following the previous definition, explain how some of the results from representation theory of groups, such as Maschke's theorem and Clifford's theorem, extend naturally to that of skew braces. They shall also give some concrete examples to illustrate that skew brace representations are more difficult to classify than group representations.
reviewed by: Enrico Jabara
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16T25
zbMATH DE Number: 7950846
zbMATH Keywords: skew braces
zbMATH Keywords: representations of finite groups
zbMATH Keywords: modules for skew braces
MaRDI profile type: Publication
DOI: 10.22108/IJGT.2024.142261.1913
description: scientific article; zbMATH DE number 7950846