J. D. H. Smith
Quantum idempotence, distributivity, and the Yang-Baxter equation

Comment.Math.Univ.Carolin. 57,4 (2016) 567-583.

Abstract:Quantum quasigroups and loops are self-dual objects that provide a~ general framework for the nonassociative extension of quantum group techniques. They also have one-sided analogues, which are not self-dual. In this paper, natural quantum versions of idempotence and distributivity are specified for these and related structures. Quantum distributive structures furnish solutions to the quantum Yang-Baxter equation.

Keywords: Hopf algebra; quantum group; quasigroup; loop; quantum Yang-Baxter equation; distributive

DOI: DOI 10.14712/1213-7243.2015.186
AMS Subject Classification: 20N05 16T25