Bol loop

Summary

A Bol loop is a loop, that is, a quasigroup with an identity element, that satisfies one of the Bol identities. A left Bol loop satisfies $a(b(ac)) = (a(ba))c$, and a right Bol loop satisfies the mirror identity $((ca)b)a = c((ab)a)$. The loops that are both left and right Bol are exactly the Moufang loops. Bol loops are named after Gerrit Bol, who met them in the study of webs in differential geometry.