On algebras and superalgebras with linear codimension growth

Abstract

We present the classification, up to PI-equivalence, of the algebras over a field of characteristic zero whose sequence of codimensions is linearly bounded. We also describe the generalization of this result in the setting of superalgebras and their graded identities. As a consequence we determine all linear functions describing the ordinary codimensions and the graded codimensions of a given algebra.