Representation theory of skew braces

Kozakai, Yuta; Tsang, Cindy

doi:10.22108/ijgt.2024.142261.1913

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	Representation theory of skew braces
International Journal of Group Theory
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 11 شهریور 1403 اصل مقاله (459.71 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2024.142261.1913
نویسندگان
Yuta Kozakai^* ¹؛ Cindy Tsang²
¹Department of Mathematics, Tokyo University of Science
²Department of Mathematics, Ochanomizu University
چکیده
According to Letourmy and Vendramin, a representation of a skew brace is a pair of representations on the same vector space, one for the additive group and the other for the multiplicative group, that satisfies a certain compatibility condition. Following their definition, we shall 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. We shall also give some concrete examples to illustrate that skew brace representations are more difficult to classify than group representations.
کلیدواژه‌ها
skew braces؛ representations of finite groups؛ modules for skew braces

مراجع
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Representation theory of skew braces