Name of Conference

Loops'23: Nonassociative Algebra

Location of Conference

Warsaw, Poland

Publication Date

2025

Publisher (if applicable)

Institute of Mathematics, Polish Academy of Sciences

Place of Publication (if applicable)

Warsaw, Poland

Document Type

Conference Paper in Published Proceedings

Department

Mathematics and Computer Science

Abstract

We study loops which are universal (that is, isotopically invariant) with respect to the property of flexibility (xy · x = x · yx). We also weaken this to semi-universality, that is, loops in which every left and right isotope is flexible, but not necessarily every isotope. One of our main results is that universally flexible, inverse property loops are Moufang loops. On the other hand, semi-universally flexible, inverse property loops are dissociative. We also examine the relationship between universally flexible loops and middle Bol loops. The paper concludes with some open problems.

Comments

Pages 35-49

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