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Representation theory of skew braces | ||
International Journal of Group Theory | ||
مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 19 مهر 1403 اصل مقاله (459.86 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 | ||
[1] E. Acri and M. Bonatto, Skew braces of size pq, Comm. Algebra, 48 no. 5 (2020) 1872–1881. [4] L. Guarnieri and L. Vendramin, Skew braces and the Yang-Baxter equation, Math. Comp., 86 no. 307 (2017) 2519–2534. | ||
آمار تعداد مشاهده مقاله: 61 تعداد دریافت فایل اصل مقاله: 42 |