Article ID Journal Published Year Pages File Type
4583835 Journal of Algebra 2016 30 Pages PDF
Abstract

Quantum quasigroups and quantum loops are self-dual objects providing a general framework for the nonassociative extension of quantum group techniques. Bialgebra reducts of Hopf algebras are quantum loops, while sufficient conditions are given for quantum loop structure to augment to a Hopf algebra. The Moufang–Hopf algebras of Benkart et al., the Hopf quasigroups and coquasigroups of Klim–Majid, and the coassociative H-bialgebras of Pérez-Izquierdo (for instance, the universal enveloping algebras of Sabinin algebras), all form quantum loops. Other quantum quasigroups offer natural nonassociative extensions of Hopf algebra constructions: quasigroup algebras, dual quasigroup algebras, and quantum couples of groups with quasigroups. Further examples include an algebra of rooted binary trees, and an algebra of skein polynomials.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
Authors
,