Modules over semisymmetric quasigroups
Abstract
The class of semisymmetric quasigroups is determined by the identity We prove that the universal multiplication group of a semisymmetric quasigroup is free over its underlying set and then specify the point-stabilizers of an action of this free group on . A theorem of Smith indicates that Beck modules over semisymmetric quasigroups are equivalent to modules over a quotient of the integral group algebra of this stabilizer. Implementing our description of the quotient ring, we provide some examples of semisymmetric quasigroup extensions. Along the way, we provide an exposition of the quasigroup module theory in more general settings.
Cite
@article{arxiv.1908.06364,
title = {Modules over semisymmetric quasigroups},
author = {Alex W. Nowak},
journal= {arXiv preprint arXiv:1908.06364},
year = {2019}
}
Comments
Presented at the Fourth Mile High Conference on Nonassociative Mathematics at University of Denver on July 31, 2017