Gouda, Yasien Ghllab; El-Deen, Alaa Hassan Nor On the trivial and nontrivial cohomology with inner symmetry groups of some classes of operator algebras. (English) Zbl 1185.46049 Int. J. Math. Anal., Ruse 3, No. 5-8, 377-384 (2009). 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. Reviewer: Samuel Smith (Philadelphia) Cited in 1 ReviewCited in 2 Documents 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 PDF BibTeX XML Cite \textit{Y. G. Gouda} and \textit{A. H. N. El-Deen}, Int. J. Math. Anal., Ruse 3, No. 5--8, 377--384 (2009; Zbl 1185.46049) Full Text: Link OpenURL