Abstract:This paper gives a brief survey of certain recently developing aspects of the study of loops and quasigroups, focussing on some of the areas that appear to exhibit the best prospects for subsequent research and for applications both inside and outside mathematics.
Keywords: quasigroup, loop, net, web, semisymmetric, Lindenbaum-Tarski duality, multiplication group, loop transversal, loop transversal code, octonions, Cayley numbers, sedenions, vector field, knot, link, quandle, surgery, Conway algebra, split extension, centraliser ring, multiplicity free, fusion rule, statistical dimension, Ising model
AMS Subject Classification: 20N05