# Flexibility law

under the flexibility law one understands the following in mathematicsRule for a linkage *

< math> A \ cdot \ left (b \ cdot A \ right) = \ left (A \ cdot b \ right) \ cdot A [/itex]

## to meaning

the flexibility law becomes important if a linkage no longer associatively and not is more commutative. It permits then still another clasping within modest framework.

## examples

### from Kommutativität flexibility follows

if the linkage * is commutative, can one by twice use of the commutative law the flexibility show:

[itex] A \ cdot \ left (b \ cdot A \ right) = \ left (b \ cdot A \ right) \ cdot A = \ left (A \ cdot b \ right) \ cdot A [/itex]

### from Assoziativität follows flexibility

is associative the linkage *, can one the flexibility show, by one in the associative law

< math> A \ cdot \ left (b \ cdot C \ right) = \ left (A \ cdot b \ right) \ cdot C [/itex]

simply C = A sets.

### the Lie clammy ones the flexibility law in

to an Lie algebra fulfills applies due to the antisymmetry of the Lieklammer

• [A, [b, A]] = − [[b, A], A] = [− [b, A], A] = [[A, b], A].

### Oktonionen

the multiplication of the Oktonionen fulfills the flexibility law.