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Classification of λ-homomorphic braces on ℤ2. / Nasybullov, T.; Novikov, I.

In: Communications in Algebra, 10.05.2025.

Research output: Contribution to journal › Article › peer-review

Harvard

Nasybullov, T & Novikov, I 2025, 'Classification of λ-homomorphic braces on ℤ2', Communications in Algebra. https://doi.org/10.1080/00927872.2025.2497412

APA

Nasybullov, T., & Novikov, I. (2025). Classification of λ-homomorphic braces on ℤ2. Communications in Algebra. https://doi.org/10.1080/00927872.2025.2497412

Vancouver

Nasybullov T, Novikov I. Classification of λ-homomorphic braces on ℤ2. Communications in Algebra. 2025 May 10. doi: 10.1080/00927872.2025.2497412

Author

Nasybullov, T. ; Novikov, I. / Classification of λ-homomorphic braces on ℤ2. In: Communications in Algebra. 2025.

BibTeX

@article{d993976d0880434f98d74813cf816f8b,
title = "Classification of λ-homomorphic braces on ℤ2",
abstract = "If (Formula presented.) is a (Formula presented.) -homomorphic brace with (Formula presented.), then the operations in this brace are given by formulas (Formula presented.) where (Formula presented.) are cpecific matrices which depend on A. Not every pair (Formula presented.) lead to a brace. In the present paper we find all possible pairs (Formula presented.) of matrices from (Formula presented.) which lead to (Formula presented.) -homomorphic braces with (Formula presented.). The obtained result gives the full classification of (Formula presented.) -homomorphic braces on (Formula presented.) which was started by Bardakov, Neshchadim and Yadav.",
keywords = "Yang-Baxter equation, skew brace, λ-homomorphic skew brace, skew brace, Yang-Baxter equation, λ-homomorphic skew brace",
author = "T. Nasybullov and I. Novikov",
note = "The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. FWNF-2022-0005).",
year = "2025",
month = may,
day = "10",
doi = "10.1080/00927872.2025.2497412",
language = "English",
journal = "Communications in Algebra",
issn = "0092-7872",
publisher = "Taylor and Francis Ltd.",

}

RIS

TY - JOUR

T1 - Classification of λ-homomorphic braces on ℤ2

AU - Nasybullov, T.

AU - Novikov, I.

N1 - The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. FWNF-2022-0005).

PY - 2025/5/10

Y1 - 2025/5/10

N2 - If (Formula presented.) is a (Formula presented.) -homomorphic brace with (Formula presented.), then the operations in this brace are given by formulas (Formula presented.) where (Formula presented.) are cpecific matrices which depend on A. Not every pair (Formula presented.) lead to a brace. In the present paper we find all possible pairs (Formula presented.) of matrices from (Formula presented.) which lead to (Formula presented.) -homomorphic braces with (Formula presented.). The obtained result gives the full classification of (Formula presented.) -homomorphic braces on (Formula presented.) which was started by Bardakov, Neshchadim and Yadav.

AB - If (Formula presented.) is a (Formula presented.) -homomorphic brace with (Formula presented.), then the operations in this brace are given by formulas (Formula presented.) where (Formula presented.) are cpecific matrices which depend on A. Not every pair (Formula presented.) lead to a brace. In the present paper we find all possible pairs (Formula presented.) of matrices from (Formula presented.) which lead to (Formula presented.) -homomorphic braces with (Formula presented.). The obtained result gives the full classification of (Formula presented.) -homomorphic braces on (Formula presented.) which was started by Bardakov, Neshchadim and Yadav.

KW - Yang-Baxter equation

KW - skew brace

KW - λ-homomorphic skew brace

KW - skew brace

KW - Yang-Baxter equation

KW - λ-homomorphic skew brace

UR - https://www.mendeley.com/catalogue/b681b114-df8e-37ee-b0ae-f84157a9cedc/

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-105008652055&origin=inward&txGid=5420d8786da5aba3245533849f4f85b8

U2 - 10.1080/00927872.2025.2497412

DO - 10.1080/00927872.2025.2497412

M3 - Article

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

ER -

ID: 68148014