Basic concepts of ternary Hopf 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.

11 pages, AmSLaTeX

References in corpus (3)

• Finite Quantum Groupoids and Their Applications
• Axioms for Weak Bialgebras
• Weak Hopf algebras and singular solutions of Quantum Yang-Baxter equation

Cited by in corpus (6)

• Notes on Cohomologies of Ternary Algebras of Associative Type
• Remarks to Glazek's results on n-ary groups
• Polyadic systems, representations and quantum groups
• (Co)associative $3$-ary (co)algebras and infinitesimal bialgebras: construction and main properties
• On Lie semiheaps and ternary principal bundles
• Hom-coassociative ternary coalgebras and infinitesimal bialgebras