Classifying the Minimal Varieties of Polynomial Growth

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Abstract

Let $\mathcal{V}$ be a variety of associative algebras generated byan algebra with $1$ over a field of characteristic zero. Thispaper is devoted to the classification of the varieties$\mathcal{V}$ which are minimal of polynomial growth (i.e., theirsequence of codimensions growth like $n^k$ but any proper subvarietygrows like $n^t$ with $t<k$). These varieties are the buildingblocks of general varieties of polynomial growth.It turns out that for $k\le 4$ there are only a finite number ofvarieties of polynomial growth $n^k$, but for each $k > 4$, thenumber of minimal varieties is at least $|F|$, the cardinality ofthe base field and we give a recipe of how to construct them.
Lingua originaleEnglish
pagine (da-a)625-640
Numero di pagine16
RivistaCANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
Volume66, no. 3
Stato di pubblicazionePublished - 2014

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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