Ternary Hopf Algebras
نویسنده
چکیده
Properties of ternary semigroups, groups and algebras are briefly reviewed. It is shown that there exist three types of ternary units. A ternary analog of deformation is shortly discussed. Ternary coalgebras are defined in the most general manner, their classification with respect to the property “to be derived” is made. Three types of coassociativity and three kinds of counits are given. Ternary Hopf algebras with skew and strong antipods are defined. Concrete examples of ternary Hopf algebras, including the Sweedler example (which has two ternary generalizations), are presented. A ternary analog of quasitriangular Hopf algebras is constructed, and ternary abstract quantum Yang–Baxter equation (together with its classical counterpart) is obtained. A ternary “pairing” of three Hopf algebras is built.
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