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 YangBaxter equation are presented.
 Publication:

arXiv eprints
 Pub Date:
 August 2013
 DOI:
 10.48550/arXiv.1308.4060
 arXiv:
 arXiv:1308.4060
 Bibcode:
 2013arXiv1308.4060D
 Keywords:

 Mathematics  Representation Theory;
 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Group Theory;
 Mathematics  Quantum Algebra;
 16T05;
 16T25;
 17A42;
 20N15;
 20F29;
 20G05;
 20G42;
 57T05
 EPrint:
 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://wwwnuclear.univer.kharkov.ua/lib/1017_3%2855%29_12_p2859.pdf