Where do these beasts show up?
I'm intending to add some examples of non-associative quasigroups later. The nonzero
octonions form a quasigroup under multiplication, and the unit octonions make the 7-sphere into a quasigroup (a Moufang loop, I think). Steiner triple systems are essentially a type of commutative quasigroup (define
a *
a =
a, and
a *
b =
c if (
a,
b,
c) is a triple). Moufang loops apparently arose in some geometric context (projective planes?), but I don't know any details about this. There are also various other types of quasigroups (IP loops, Bol loops, etc.) that have been studied, but I don't know where they arise. --
Zundark, 2001-09-04
How do Quasigroups relate to cwatsets?
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