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…
Conjecture on Maximal Sublattices of Finite Semidistributive Lattices and Beyond
K. Adaricheva, A. Mata, S. Silberger +1
We study maximal sublattices of finite semidistributive lattices via their complements. We focus on the conjecture that such complements are always intervals, which is known to be…
Dihedral solutions of the set theoretical Yang-Baxter equation
Alex W. Nowak, Anna Zamojska-Dzienio
We introduce the notion of a \emph{braided dihedral set} (BDS) to describe set-theoretical solutions of the Yang-Baxter equation (YBE) that furnish representations of the infinite…
Barycentric algebras -- convexity and order
Anna Zamojska-Dzienio
This is the abstract of a series of lectures given during the XIIIth School on Geometry and Physics, Bialystok (Poland), in July 2024. In this minicourse, we first examine the alge…
Partitions of unity and barycentric algebras
Anna Zamojska-Dzienio
Barycentric coordinates provide solutions to the problem of expressing an element of a compact convex set as a convex combination of a finite number of extreme points of the set. T…