Quandle (knot theory)
(Redirected from Racks and quandles)
In mathematics, a rack and a quandle in knot theory are sets with a binary operation mimicking the three Reidemeister moves of diagram manipulation.
Suppose that the binary operation is written <math>a*b<math>. Then the three laws for a quandle are
- <math>a*a=a<math>
- <math>x\to x*a<math> is a bijection for all <math>a<math>
- <math>(a*b)*c=(a*c)*(b*c)<math>
A rack is more general than a quandle: it satisfies only the two last laws.
An alternative definition of a rack is that it is a set with a binary operation in which multiplication on one side is an automorphism.
Categories: Knot theory | Abstract algebra