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 </math>

Table of contents

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:

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


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 </math>

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.

see also

alternative body, associative law, Jordan algebra, commutative law, Lie algebra, Moufang identities, Oktonionen

 

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