Classification of generalized Alexander quandles
Akihiro Higashitani, Seiichi Kamada, Jin Kosaka, Hirotake Kurihara
TL;DR
This paper offers a new way to classify generalized Alexander quandles using group theory, extending previous results, and provides enumeration for groups up to order 127.
Contribution
It introduces a novel characterization of isomorphism classes of generalized Alexander quandles based on groups and automorphisms, expanding prior work.
Findings
New characterization of quandle isomorphism classes
Enumeration of generalized Alexander quandles up to order 127
Extended previous classification results
Abstract
The aim of this paper is to provide a new characterization of isomorphism classes of generalized Alexander quandles in terms of the underlying groups and their automorphisms. This extends the previous result [4, Theorem 1.4]. Additionally, we compute the number of generalized Alexander quandles up to quandle isomorphism arising from groups up to order 127 and their group automorphisms.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Code & Models
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsRings, Modules, and Algebras · semigroups and automata theory · Advanced Algebra and Logic