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arXiv · 0705.4333

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

Ebrahim Samei
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Abstract

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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Ebrahim Samei. 2007-05-30. On local properties of Hochschild cohomology of a C$^*$- algebra. https://doi.org/10.1017/s1446788708000049

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