## On the trivial and nontrivial cohomology with inner symmetry groups of some classes of operator algebras.(English)Zbl 1185.46049

The authors prove vanishing and non-vanishing results for certain specialized cohomology theories (e.g., dihedral and cyclic) applied to Banach algebras. For example, they prove that the reflexive and dihedral cohomology of a stable $$C^*$$-algebra vanishes while the dihedral cohomology of a commutative Banach algebra $$A$$ having an involution and satisfying $$\mathrm{codim}A^2 > 1$$ does not.

### MSC:

 46M20 Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) 46H05 General theory of topological algebras

### Keywords:

dihedral cohomology; cyclic cohomology; operator algebras
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