Cocommutative

Cocommutative

Cocommutativité

En mathématiques, la cocommutativité est une notion duale de la notion de commutativité.

Définition

Soit (A,Δ) une bialgèbre. Pour tout x appertenant à A, on note  \Delta(x)= \sum_k x_k^{(1)} \otimes x_k^{(2)}. La bialgèbre A est dite cocommutative si :

\forall x \in A,\ \sum_k x_k^{(1)} \otimes x_k^{(2)}=\sum_k x_k^{(2)} \otimes x_k^{(1)}
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