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

Gouda, Yasien Ghllab; El-Deen, Alaa Hassan Nor

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)

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