Symmetric skew braces and brace systems | Sciact - Система учета научной деятельности ИМ СО РАН

Symmetric skew braces and brace systems Научная публикация

Журнал

Forum Mathematicum
ISSN: 0933-7741 , E-ISSN: 1435-5337

Вых. Данные

Год: 2023, Том: 35, Номер: 3, Страницы: 713-738 Страниц : 26 DOI: 10.1515/forum-2022-0134

Ключевые слова

Skew left brace; symmetric skew brace

Авторы

Bardakov V.G. ^1,2,3 , Neshchadim M.V. ^1,3 , Yadav Manoj K. ⁴

Организации

1	Sobolev Institute of Mathematics, pr. ak. Koptyuga 4, Novosibirsk, 630090;
2	Novosibirsk State Agrarian University, Dobrolyubova street, 160, Novosibirsk, 630039;
3	Regional Scientific and Educational Mathematical Center of Tomsk State University, 36 Lenin Ave., Tomsk, Russia
4	Harish-Chandra Research Institute, A CI of Homi Bhabha National Institute, Chhatnag Road, Jhunsi, Prayagraj-211 019, India

Информация о финансировании (2)

1	Институт математики им. С.Л. Соболева СО РАН	FWNF-2022-0009
2	Министерство науки и высшего образования РФ	075-02-2022-884

For a skew left brace (G, center dot, o), the map lambda : (G, o)-> Aut(G, center dot ), a (sic) lambda(a), where lambda(a)(b) = a(-1 )center dot (a o b) for all a, b E G, is a group homomorphism. Then lambda can also be viewed as a map from (G, center dot ) to Aut(G, center dot ), which, in general, may not be a homomorphism. A skew left brace will be called lambda-anti-homomorphic (lambda-homomorphic) if lambda : (G, center dot )->, Aut(G, center dot ) is an anti-homomorphism (a homomorphism). We mainly study such skew left braces. We device a method for constructing a class of binary operations on a given set so that the set with any two such operations constitutes a lambda-homomorphic symmetric skew brace. Most of the constructions of symmetric skew braces dealt with in the literature fall in the framework of our construction. We then carry out various such constructions on specific infinite groups.

Bardakov V.G. , Neshchadim M.V. , Yadav M.K.
Symmetric skew braces and brace systems
Forum Mathematicum. 2023. V.35. N3. P.713-738. DOI: 10.1515/forum-2022-0134 WOS Scopus OpenAlex

Поступила в редакцию:	26 апр. 2022 г.
Опубликована online:	28 февр. 2023 г.
Опубликована в печати:	1 мая 2023 г.

Web of science:	WOS:000940844800001
Scopus:	2-s2.0-85149574303
OpenAlex:	W4322494284

БД	Цитирований
Web of science	2
Scopus	3
OpenAlex	2