| Local Cocycle $3$-Hom-Lie Bialgebras and $3$-Lie Classical Hom-Yang-Baxter Equation |
| Received:November 22, 2016 Revised:August 04, 2017 |
| Key Words:
local cocycle $3$-Hom-Lie bialgebra $3$-Lie CHYBE coboundary condition
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11047030) and the Science and Technology Program of Henan Province (Grant No.152300410061). |
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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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