Varieties of associative algebras with quadratic codimension growth

Abstract

We classify, up to PI-equivalence, associative algebras over a field of characteristic zero whose codimension sequences have quadratic growth. More precisely, making use of fundamental algebras, we prove that every such algebra is PI-equivalent to a finite direct sum of algebras generating minimal varieties of at most quadratic codimension growth, together with a possible nilpotent summand.