Polynomial growth and star-varieties

Minimal star-varieties of polynomial growth and bounded colength

“…The purpose of this section is to study the sequences of * -cocharacters, * -codimensions and * -colengths of the minimal subvarieties of polynomial growth of the varieties of almost polynomial growth, which are classified in [20].…”

“…, the subalgebra of U T 4 with the reflection involution, i.e., the involution obtained by reflecting a matrix along its secondary diagonal: if a = α(e We start by presenting * -algebras belonging to the variety generated by D and generating minimal varieties of polynomial growth (see [20]).…”

“…In [20] the authors completely classify all subvarieties of the varieties var * (D) and var * (M ). They also classify all their minimal subvarieties of polynomial growth.…”

“…As a consequence the algebras D and M generate the only varieties of almost polynomial growth. In [20] the authors completely classify all subvarieties and all minimal subvarieties of the varieties var * (D) and var * (M ). In this paper we exhibit the decompositions of the * -cocharacters of all minimal subvarieties of var * (D) and var * (M ) and compute their * -colengths.…”

On algebras of polynomial codimension growth

“…Much effort has been put into the study of varieties V of polynomial growth, i.e., such that c n (V) is polynomially bounded [5,12,[17][18][19][20][21].…”