Uniform bounds for point cohomology of and related algebras

The point cohomology of the convolution algebra ℓ 1 ( Z + ) is known to vanish in degrees 2 and above. We sharpen this result by obtaining splitting maps whose norms are bounded independently of the choice of point module. Our construction is a by-product of new estimates on projectivity constants of maximal ideals in ℓ 1 ( Z + ) . Analogous results are obtained for some other L 1 -algebras which arise from ‘rank one’ subsemigroups of R + .