Smooth cohomology of $ C^* $-algebras
Massoud Amini, Ahmad Shirinkalam

TL;DR
This paper introduces a new notion of smooth cohomology for $ C^* $-algebras with faithful traces and establishes an equivalence between smooth and standard cohomology under certain conditions involving dual operator bimodules.
Contribution
It defines smooth cohomology for $ C^* $-algebras with traces and proves an isomorphism between smooth and standard first cohomology groups for specific bimodules.
Findings
Smooth cohomology is well-defined for $ C^* $-algebras with faithful traces.
First smooth cohomology coincides with standard cohomology for certain bimodules.
The result applies to $ C^* $-algebras with ultra-weakly closed subalgebras and normal dual bimodules.
Abstract
We define a notion of smooth cohomology for -algebras which admit a faithful trace. We show that if is a -algebra with a faithful normal trace on the ultra-weak closure of , and is a normal dual operatorial -bimodule, then the first smooth cohomology of is equal to , where is a closed submodule of consisting of smooth elements.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Algebraic structures and combinatorial models
