Varieties of Algebras of Polynomial Growth

La Mattina, Daniela

Bollettino della Unione matematica italiana, Série 9, Tome 1 (2008) no. 3, pp. 525-538

Résumé

Let $\mathcal{V}$ be a proper variety of associative algebras over a field $F$ of characteristic zero. It is well-known that $\mathcal{V}$ can have polynomial or exponential growth and here we present some classification results of varieties of polynomial growth. In particular we classify all subvarieties of the varieties of almost polynomial growth, i.e., the subvarieties of $\operatorname{\textbf{var}}(G)$ and $\operatorname{\textbf{var}}(UT_2)$, where $G$ is the Grassmann algebra and $UT_2$ is the algebra of $2 \times 2$ upper triangular matrices.