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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).

Author to whom correspondence should be addressed

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

Full text: PDF file (616 kB)
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English version:
Sbornik: Mathematics, 2018, 209:6, 901–918

Bibliographic databases:

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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