Izvorni znanstveni članak

Smooth cohomology of $C^{\ast }-algebras$

Masoud Amini ; Department of Mathematics, Tarbiat Modares University, P.O Box 14 115-175, Tehran, Iran
Ahmad Shirinkalam ; Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran

Sažetak

We define a notion of smooth cohomology for $C^{\ast }$-algebras which admit a faithful trace. We show that if $\text{A}\subseteq B(\text{h})$ is a $C^{\ast }$-algebra with a faithful normal trace $\tau$ on the ultra-weak closure $\overline{A}$ of $\mathcal{A}$, and $X$ is a normal dual operatorial $\overline{A}$-bimodule, then the first smooth cohomology ${\mathcal{H}}_s^1(\mathcal{A},X)$ of $\mathcal{A}$ is equal to ${\mathcal{H}}^1(\mathcal{A},X_{\tau })$, where $X_{\tau }$ is a closed submodule of $X$ consisting of smooth elements.

Ključne riječi

smooth cohomology; group action; equivariant bimodule; faithful trace

Hrčak ID:

252598

URI

https://hrcak.srce.hr/252598

Datum izdavanja:

10.3.2021.

Posjeta: 923 *