Subquandles of affine quandles

JOURNAL OF ALGEBRA

卷:510

Article

Jedlicka, Premysl¹  Pilitowska, Agata²  Stanovsky, David³  Zamojska-Dzienio, Anna² 

[1] Czech Univ Life Sci, Fac Engn, Dept Math, Karnycka 129, Prague 16521 6, Czech Republic

[2] Warsaw Univ Technol, Fac Math & Informat Sci, Koszykowa 75, PL-00662 Warsaw, Poland

[3] Charles Univ Prague, Fac Math & Phys, Dept Algebra, Sokolovska 83, Prague 18675 8, Czech Republic

关键词: Quandles;    Medial quandles;    Affine quandles;    Commutator theory;    Abelian algebras;    Quasi-affine algebras;    Quasi-affine modes;   

DOI  :  10.1016/j.jalgebra.2018.06.001

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free