24 citations · 65 across the 15 of their papers we have counts for
5 papers · 1 filter
In Search of Homology for Quasigroups of Bol-Moufang Type
Anthony Christiana, Ben Clingenpeel, Huizheng Guo +3
We initiate (co)homology theory for quasigroups of Bol-Moufang type based on analysis of their extensions by affine quasigroups of the same type. We use these extensions to define…
Indecomposable involutive solutions of the Yang-Baxter equation of multipermutational level 2 with abelian permutation group
Přemysl Jedlička, Agata Pilitowska, Anna Zamojska-Dzienio
We present a construction of all finite indecomposable involutive solutions of the Yang-Baxter equation of multipermutational level at most 2 with abelian permutation group. As a c…
Knot-theoretic ternary groups
Maciej Niebrzydowski, Agata Pilitowska, Anna Zamojska-Dzienio
We describe various properties and give several characterizations of ternary groups satisfying two axioms derived from the third Reidemeister move in knot theory. Using special att…
Subquandles of affine quandles
Přemysl Jedlička, Agata Pilitowska, David Stanovský +1
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 d…
The structure of medial quandles
Přemysl Jedlička, Agata Pilitowska, David Stanovský +1
Medial quandles are represented using a heterogeneous affine structure. As a consequence, we obtain numerous structural properties, including enumeration of isomorphism classes of…