We give a rigorous proof that the (codimension one) Connes-Moscovici Hopf algebra HCM is isomorphic to a bicrossproduct Hopf algebra linked to a group factorisation of the diffeomorphism group Diff(R). We construct a second bicrossproduct UCM equipped with a nondegenerate dual pairing with HCM. We give a natural quotient Hopf algebra kλ[Heis] of HCM and Hopf subalgebra Uλ(heis) of UCM which aga...

1 2 CONNES AND MARCOLLI

In this paper, we provide several characterisations for uniform amenability concerning a family of finitely generated groups. More precisely, show that the Hulanicki–Reiter condition can be weakened in directions, including cardinalities supports and certain operator norms.

Let A be a Banach algebra and I closed ideal of A. We say that is amenable relative to I, if A/I an algebra. study the amenability algebras investigate triangular associated locally compact groups. generalize some previous known results by applying concept algebras, especially, we present generalization Johnson?s theorem in amenability.

Around 1980 Connes extended the notions of geometry to the noncommutative setting. Since then non-commutative geometry has turned into a very active area of mathematical research. As a first non-trivial example of a noncommutative manifold Connes discussed subalgebras of rotation algebras, the socalled non-commutative tori. In the last two decades researchers have unrevealed the relevance of no...