Symmetric skew braces and brace systems

Symmetric skew braces and brace systems Full article

Journal

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

Output data

Year: 2023, Volume: 35, Number: 3, Pages: 713-738 Pages count : 26 DOI: 10.1515/forum-2022-0134

Tags

Skew left brace; symmetric skew brace

Authors

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

Affiliations

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

Funding (2)

1	Sobolev Institute of Mathematics	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

Submitted:	Apr 26, 2022
Published online:	Feb 28, 2023
Published print:	May 1, 2023

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

DB	Citing
Web of science	2
Scopus	3
OpenAlex	2