Classification of λ-homomorphic braces on ℤ2 | Sciact - Система учета научной деятельности ИМ СО РАН

Classification of λ-homomorphic braces on ℤ2 Научная публикация

Журнал

Communications in Algebra
ISSN: 0092-7872 , E-ISSN: 1532-4125

Вых. Данные

Год: 2025, DOI: 10.1080/00927872.2025.2497412

Ключевые слова

λ-homomorphic skew brace, skew brace, Yang-Baxter equation

Авторы

Nasybullov T. ^1,2 , Novikov I. ¹

Организации

1	Novosibirsk State University, Novosibirsk, Russia;
2	Sobolev Institute of Mathematics, Novosibirsk, Russia

Информация о финансировании (1)

Институт математики им. С.Л. Соболева СО РАН

FWNF-2022-0005

If A=(A,circle plus,circle dot) is a lambda-homomorphic brace with (A,circle plus)=Z(2), then the operations in this brace are given by formulas (a1 a2)circle plus(b1 b2)=(a1+b1a2+b2),(a1 a2)circle dot(b1 b2)=(a1 a2)+phi(a1)psi(a2)(b1 b2), where phi,psi is an element of GL2(Z) are cpecific matrices which depend on A. Not every pair (phi,psi) lead to a brace. In the present paper we find all possible pairs (phi,psi) of matrices from GL2(Z) which lead to lambda-homomorphic braces with (A,circle plus)=Z(2). The obtained result gives the full classification of lambda-homomorphic braces on Z(2) which was started by Bardakov, Neshchadim and Yadav.

Nasybullov T. , Novikov I.
Classification of λ-homomorphic braces on ℤ2
Communications in Algebra. 2025. DOI: 10.1080/00927872.2025.2497412 WOS OpenAlex

Поступила в редакцию:	15 окт. 2024 г.
Принята к публикации:	8 апр. 2025 г.
Опубликована online:	10 мая 2025 г.

Web of science:	WOS:001485069100001
OpenAlex:	W4410252509

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