English

Basic concepts of ternary Hopf algebras

Quantum Algebra 2007-05-23 v1 High Energy Physics - Theory Mathematical Physics Group Theory math.MP Rings and Algebras

Abstract

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.

Keywords

Cite

@article{arxiv.math/0306208,
  title  = {Basic concepts of ternary Hopf algebras},
  author = {Andrzej Borowiec and Wieslaw A. Dudek and Steven Duplij},
  journal= {arXiv preprint arXiv:math/0306208},
  year   = {2007}
}

Comments

11 pages, AmSLaTeX

R2 v1 2026-07-22T16:55:24.288Z