Semigroup graded algebras and codimension growth of graded polynomial identities Vrije Universiteit Brussel
We show that if T is any of four semigroups of two elements that are not groups, there exists a finite dimensional associative T-graded algebra over a field of characteristic 0 such that the codimensions of its graded polynomial identities have a non-integer exponent of growth. In particular, we provide an example of a finite dimensional graded-simple semigroup graded algebra over an algebraically closed field of characteristic 0 with a ...