Local Cocycle $3$-Hom-Lie Bialgebras and $3$-Lie Classical Hom-Yang-Baxter Equation
Received:November 22, 2016  Revised:August 04, 2017
Key Word: local cocycle $3$-Hom-Lie bialgebra   $3$-Lie CHYBE   coboundary condition  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11047030) and the Science and Technology Program of Henan Province (Grant No.152300410061).
Author NameAffiliation
Mengping WANG School of Mathematics and Statistics, Henan University, Henan 475004, P. R. China 
Linli WU School of Mathematics and Statistics, Henan University, Henan 475004, P. R. China 
Yongsheng CHENG School of Mathematics and Statistics, Henan University, Henan 475004, P. R. China 
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Abstract:
      In this paper, we introduce $3$-Hom-Lie bialgebras whose compatibility conditions between the multiplication and comultiplication are given by local cocycle conditions. We study a twisted $3$-ary version of the Yang-Baxter Equation, called the $3$-Lie classical Hom-Yang-Baxter Equation ($3$-Lie CHYBE), which is a general form of $3$-Lie classical Yang-Baxter Equation and prove that the bialgebras induced by the solutions of $3$-Lie CHYBE induce the coboundary local cocycle $3$-Hom-Lie bialgebras.
Citation:
DOI:10.3770/j.issn:2095-2651.2017.06.004
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