Isotropy Groups of Free Racks and Quandles

2020/10/19 by Parker, Jason
#Category Theory (math.CT) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2010.09837

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.

Related

• The homotopy types of free racks and quandles
• Quasimorphisms of free products of racks and quandles
• Homogeneous quandles with abelian inner automorphism groups
• Enumerating finite racks, quandles and kei
• On the Cycle Structure of Finite Racks and Quandles