3-HOM-LIE SUPERBIALGEBRAS AND 3-HOM-LIE CLASSICAL YANG-BAXTER EQUATIONS

3 -Lie algebras are in close relationships with many fields. In this paper we are concerned with the study of 3-Hom-Lie super algebras, the concepts of 3-Hom-Lie coalgebras and how they make a 3-Hom-Lie superbialgebras, we study the structures of such categories of algebras and the relationships between each others. We study a super twisted 3ary version of the Yang -Baxter equation, called the super 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 superbialgebras induced by the solutions of the super 3 -Lie CHYBE induce the cob oundary local cocycle 3-Hom-Lie superbialgebras.