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In this paper, we introduce 3-Hom-Lie bialgebras whose compatibilityconditions between the multiplication and comultiplication are given by localcocycle conditions. We study a twisted 3-ary version of the Yang-BaxterEquation, called the 3-Lie classical HomYang-Baxter Equation (3-Lie CHYBE),which is a general form of 3-Lie classical YangBaxter Equation studied in [2]and prove that the bialgebras induced by the solutions of 3-Lie CHYBE inducethe coboundary local cocycle 3-Hom-Lie bialgebras.

Local cocycle 3-Hom-Lie Bialgebras and 3-Lie Classical Hom-Yang-Baxter Equation