On local properties of Hochschild cohomology of a C$^*$- algebra

Details On local properties of Hochschild cohomology of a C$^*$- algebra On local properties of Hochschild cohomology of a C$^*$- algebra

2007-05-30

arxiv.org/abs/0705.4333v1

Mathematics

Operator Algebras

13 pages

Scientific paper

Let $A$ be a C$^*$-algebra, and let $X$ be a Banach $A$-bimodule. B. E.
Johnson showed that local derivations from $A$ into $X$ are derivations. We
extend this concept of locality to the higher cohomology of a $C^*$-algebra
%for $n$-cocycles from $A^{(n)}$ into $X$ and show that, for every $n\in \N$,
bounded local $n$-cocycles from $A^{(n)}$ into $X$ are $n$-cocycles.

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