Finitely Stable Racks and Rack Representations
Quandles, racks, representations, 57M25, 20E22, 22E41, 20G05
Digital Object Identifier (DOI)
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.
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Citation / Publisher Attribution
Communications in Algebra, v. 46, issue 11, p. 4787-4802
Scholar Commons Citation
Elhamdadi, Mohamed and Moutuou, El-kaïoum M., "Finitely Stable Racks and Rack Representations" (2018). Mathematics and Statistics Faculty Publications. 142.