On λ-homomorphic skew braces

Результат исследования: Научные публикации в периодических изданияхстатьярецензирование

Аннотация

For a skew left brace (G,⋅,∘), the map λ:(G,∘)→Aut(G,⋅),a↦λa, where λa(b)=a−1⋅(a∘b) for all a,b∈G, is a group homomorphism. Then λ can also be viewed as a map from (G,⋅) to Aut(G,⋅), which, in general, may not be a homomorphism. We study skew left braces (G,⋅,∘) for which λ:(G,⋅)→Aut(G,⋅) is a homomorphism. Such skew left braces will be called λ-homomorphic. We formulate necessary and sufficient conditions under which a given homomorphism λ:(G,⋅)→Aut(G,⋅) gives rise to a skew left brace, which, indeed, is λ-homomorphic. As an application, we construct a lot of skew left braces (of infinite order) on free groups and free abelian groups. We prove that any λ-homomorphic skew left brace is an extension of a trivial skew brace by a trivial skew brace. Special emphasis is given on λ-homomorphic skew left brace for which the image of λ is cyclic. We also obtain set-theoretic solutions of the Yang-Baxter equation corresponding to the skew braces we construct in this paper.

Язык оригиналаанглийский
Номер статьи106961
ЖурналJournal of Pure and Applied Algebra
Том226
Номер выпуска6
DOI
СостояниеОпубликовано - июн 2022

Предметные области OECD FOS+WOS

  • 1.01 МАТЕМАТИКА

Fingerprint

Подробные сведения о темах исследования «On λ-homomorphic skew braces». Вместе они формируют уникальный семантический отпечаток (fingerprint).

Цитировать