In [3], Oka and the second author considered the cohomology of the second Morava stabilizer algebra to study nontriviality of the products of beta elements of the stable homotopy groups of spheres. In this paper, we use the cohomology of the third Morava stabilizer algebra to find nontrivial products of Greek letters of the stable homotopy groups of spheres: α1γt, β2γt, 〈α1, α1, β p/p〉γtβ1 and ...

Let C be a coalgebra over a field k and A its dual algebra. The category of C-comodules is equivalent to a category of A-modules. We use this to interpret the cotensor product M N of two comodules in terms of the appropriate Hochschild cohomology of the A-bimodule M ⊗N , when A is finite-dimensional, profinite, graded or differential-graded. The main applications are to Galois cohomology, comod...

We give a construction of Connes-Moscovici’s cyclic cohomology for any Hopf algebra equipped with a character. Furthermore, we introduce a non-commutative Weil complex, which connects the work of Gelfand and Smirnov with cyclic cohomology. We show how the Weil complex arises naturally when looking at Hopf algebra actions and invariant higher traces, to give a non-commutative version of the usua...

Let A be a Banach algebra, not necessarily unital, and let B be a closed subalgebra of A. We establish a connection between the Banach cyclic cohomology group HC(A) of A and the Banach B-relative cyclic cohomology group HCnB(A) of A. We prove that, for a Banach algebra A with a bounded approximate identity and an amenable closed subalgebra B of A, up to topological isomorphism, HC(A) = HCnB(A) ...

We characterize Hopf spaces with finitely generated cohomology as algebra over the Steenrod algebra. We “deconstruct” the original space into an Hspace Y with finite mod p cohomology and a finite number of p-torsion EilenbergMac Lane spaces. One reconstructs X from Y by taking extensions by principal H-fibrations. We give a precise description of homotopy commutative H-spaces in this setting an...