On algebras of polynomial codimension growth

Let A be an associative algebra over a field F of characteristic zero and let c_n(A), n = 1,2,..., be the sequence of codimensions of A. It is well-known that c_n(A), n = 1,2,..., cannot have intermediate growth, i.e., either is polynomially bounded or grows exponentially. Here we present some results on algebras whose sequence of codimensions is polynomially bounded.