Polyadic systems, representations and quantum groups
Abstract
Polyadic systems and their representations are reviewed and a classification of general polyadic systems is presented. A new multiplace generalization of associativity preserving homomorphisms, a 'heteromorphism' which connects polyadic systems having unequal arities, is introduced via an explicit formula, together with related definitions for multiplace representations and multiactions. Concrete examples of matrix representations for some ternary groups are then reviewed. Ternary algebras and Hopf algebras are defined, and their properties are studied. At the end some ternary generalizations of quantum groups and the Yang-Baxter equation are presented.
Cite
@article{arxiv.1308.4060,
title = {Polyadic systems, representations and quantum groups},
author = {Steven Duplij},
journal= {arXiv preprint arXiv:1308.4060},
year = {2018}
}
Comments
51 pages, 1 table, 1 figure, amsart. In this version: small changes. For concise (without commutative diagrams, quiver diagrams, table and figure) journal version, see http://www-nuclear.univer.kharkov.ua/lib/1017_3%2855%29_12_p28-59.pdf