English

Isotropy Groups of Free Racks and Quandles

Category Theory 2020-10-30 v2 Group Theory

Abstract

In this article, we characterize the (covariant) isotropy groups of free, finitely generated racks and quandles. As a consequence, we show that the usual inner automorphisms of such racks and quandles are precisely those automorphisms that are "coherently extendible". We then use this result to compute the global isotropy groups of the categories of racks and quandles, i.e. the automorphism groups of the identity functors of these categories.

Keywords

Cite

@article{arxiv.2010.09837,
  title  = {Isotropy Groups of Free Racks and Quandles},
  author = {Jason Parker},
  journal= {arXiv preprint arXiv:2010.09837},
  year   = {2020}
}

Comments

Added new reference and discussion of its results