Title

Finitely Stable Racks and Rack Representations

Document Type

Article

Publication Date

2018

Keywords

Quandles, racks, representations, 57M25, 20E22, 22E41, 20G05

Digital Object Identifier (DOI)

https://doi.org/10.1080/00927872.2018.1455102

Abstract

We define a new class of racks, called finitely stable racks, which, to some extent, share various flavors with Abelian groups. Characterization of finitely stable Alexander quandles is established. Further, we study twisted rack dynamical systems, construct their cross-products, and introduce representation theory of racks and quandles. We prove several results on the strong representations of finite connected involutive racks analogous to the properties of finite Abelian groups. Finally, we define the Pontryagin dual of a rack as an Abelian group which, in the finite involutive connected case, coincides with the set of its strong irreducible representations.

Was this content written or created while at USF?

Yes

Citation / Publisher Attribution

Communications in Algebra, v. 46, issue 11, p. 4787-4802

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