Varieties of special Jordan algebras of almost polynomial growth

摘要

Let J be a special Jordan algebra and let c(n)(J) be its corresponding codimension sequence. The aim of this paper is to prove that in case J is finite dimensional, such a sequence is polynomially bounded if and only if the variety generated by J does not contain U J(2), the special Jordan algebra of 2 x 2 upper triangular matrices. As an immediate consequence, we prove that U J(2) is the only finite dimensional special Jordan algebra that generates a variety of almost polynomial growth. (C) 2019 Elsevier Inc. All rights reserved.