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Mat. Sb., 2018, Volume 209, Number 6, Pages 128–145 (Mi msb8863)  

Solutions of the BiHom-Yang-Baxter equation

X. Fanga, W. Liub

a Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing, China
b Department of Mathematics, Yuanpei College of Shaoxing University, Shaoxing, China

Abstract: In this paper we extend the Yang-Baxter equation (YBE) into the setting of BiHom-structures and the BiHom-Yang-Baxter equation (BHYBE) is introduced. Two methods for constructing solutions of the BHYBE are discussed, one from Hopf algebras and the other from BiHom-Lie algebras. Finally, as an application, we show that a solution of the BHYBE can generate a representation of the braid group.
Bibliography: 34 titles.

Keywords: BiHom-Yang-Baxter equation, BiHom-Lie algebra, BiHom-associative algebra.

Funding Agency Grant Number
Natural Science Foundation of Zhejiang Province LY14A010006
National Natural Science Foundation of China 11571239
X.-L. Fang's research was carried out with the support of the Natural Science Foundation of Zhejiang Province (grant no. LY14A010006) and the National Natural Science Foundation of China (grant no. 11571239).


DOI: https://doi.org/10.4213/sm8863

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English version:
Sbornik: Mathematics, 2018, 209:6, 901–918

Bibliographic databases:

Document Type: Article
UDC: 512.667.7
MSC: 16T05, 16T15, 16T25
Received: 15.11.2016 and 02.07.2017

Citation: X. Fang, W. Liu, “Solutions of the BiHom-Yang-Baxter equation”, Mat. Sb., 209:6 (2018), 128–145; Sb. Math., 209:6 (2018), 901–918

Citation in format AMSBIB
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