turkmath.org

We are interested in semigroup algebras sitting on a semigroup - both the algebraic and analytic versions. It is surprisingly difficult to decide when these algebras are semisimple. We shall discuss this, explaining terms. A key test case for our question is to take algebras sitting on the Stone–Cech compactification of the natural numbers. I shall explain how this compactification becomes a semigroup, and note that the answer to our question probably depends on the settheoretic assumptins that we make.