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Sbornik: Mathematics, 2018, Volume 209, Issue 6, Pages 901–918
DOI: https://doi.org/10.1070/SM8863 (Mi sm8863) 		 
This article is cited in 4 scientific papers (total in 4 papers)

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
English version PDF (531 kB) Citations (4)
References:
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DOI: https://doi.org/10.1070/SM8863
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).
Received: 15.11.2016 and 02.07.2017
Russian version:
Matematicheskii Sbornik, 2018, Volume 209, Number 6, Pages 128–145
DOI: https://doi.org/10.4213/sm8863
Bibliographic databases:
Document Type: Article
UDC: 512.667.7
MSC: 16T05, 16T15, 16T25
Language: English
Original paper language: Russian
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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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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