Search results for "almost polynomial growth"
showing 2 items of 2 documents
Identities of *-superalgebras and almost polynomial growth
2015
We study the growth of the codimensions of a *-superalgebra over a field of characteristic zero. We classify the ideals of identities of finite dimensional algebras whose corresponding codimensions are of almost polynomial growth. It turns out that these are the ideals of identities of two algebras with distinct involutions and gradings. Along the way, we also classify the finite dimensional simple *-superalgebras over an algebraically closed field of characteristic zero.
Varieties of special Jordan algebras of almost polynomial growth
2019
Abstract 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 × 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.