Ternary n-weak amenability of C*-algebras and group algebras

Abstract

We introduce the notion of ternary $n$-weak amenability for every $n\in\mathbb{N}$, in the context of triple systems and prove that every group algebra of a discrete abelian group and every commutative unital C$^*$-algebras are ternary $n$-weakly amenable. These results present a somehow unified extension of the previous ternary weak amenability results and $n$-weak amenability results in the category of triple systems and Banach algebras, respectively.