Basic concepts of ternary Hopf algebras

Details Basic concepts of ternary Hopf algebras Basic concepts of ternary Hopf algebras

2003-06-12

arxiv.org/abs/math/0306208v1

Journal of Kharkov National University, ser. Nuclei, Particles and Fields, v. 529, N 3(15) (2001) pp. 21--29

Mathematics

Quantum Algebra

11 pages, AmSLaTeX

Scientific paper

The theory of ternary semigroups, groups and algebras is reformulated in the abstract arrow language. Then using the reversing arrow ansatz we define ternary comultiplication, bialgebras and Hopf algebras and investigate their properties. The main property "to be binary derived" is considered in detail. The co-analog of Post theorem is formulated. It is shown that there exist 3 types of ternary coassociativity, 3 types of ternary counits and 2 types of ternary antipodes. Some examples are also presented.

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