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.
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