Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8895855 | Journal of Algebra | 2018 | 30 Pages |
Abstract
A quandle will be called quasi-affine, if it embeds into an affine quandle. Our main result is a characterization of quasi-affine quandles, by group-theoretic properties of their displacement group, by a universal algebraic condition coming from the commutator theory, and by an explicit construction over abelian groups. As a consequence, we obtain efficient algorithms for recognizing affine and quasi-affine quandles, and we enumerate small quasi-affine quandles. We also prove that the “abelian implies quasi-affine” problem of universal algebra has affirmative answer for the class of quandles.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
PÅemysl JedliÄka, Agata Pilitowska, David Stanovský, Anna Zamojska-Dzienio,