Classification of λ-homomorphic braces on ℤ2 Full article
| Journal |
Communications in Algebra
ISSN: 0092-7872 , E-ISSN: 1532-4125 |
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| Output data | Year: 2025, DOI: 10.1080/00927872.2025.2497412 | ||||
| Tags | λ-homomorphic skew brace, skew brace, Yang-Baxter equation | ||||
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0005 |
Abstract:
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.
Cite:
Nasybullov T.
, Novikov I.
Classification of λ-homomorphic braces on ℤ2
Communications in Algebra. 2025. DOI: 10.1080/00927872.2025.2497412 WOS OpenAlex
Classification of λ-homomorphic braces on ℤ2
Communications in Algebra. 2025. DOI: 10.1080/00927872.2025.2497412 WOS OpenAlex
Dates:
| Submitted: | Oct 15, 2024 |
| Accepted: | Apr 8, 2025 |
| Published online: | May 10, 2025 |
Identifiers:
| Web of science: | WOS:001485069100001 |
| OpenAlex: | W4410252509 |
Citing:
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