a survey of simplicial cohomology for semigroup algebras

in this survey, we investigate the higher simplicial cohomology groups of the convolution algebra ℓ¹(s) for various semigroups s. the classes of semigroups considered are semilattices, clifford semigroups, regular rees semigroups and the additive semigroups of integers greater than a for some integer a. our results are of two types: in some cases, we show that some cohomology groups are 0, while in some other cases, we show that some cohomology groups are banach spaces.