Geodesic
Classifying the Minimal Varieties of Polynomial Growth
Canadian journal of mathematics, Tome 66 (2014) no. 3, pp. 625-640

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DOI

Let $\mathcal{V}$ be a variety of associative algebras generated by an algebra with 1 over a field of characteristic zero. This paper is devoted to the classification of the varieties $\mathcal{V}$ that are minimal of polynomial growth (i.e., their sequence of codimensions grows like ${{n}^{k}}$ , but any proper subvariety grows like ${{n}^{t}}$ with $t\,<\,k$ ). These varieties are the building blocks of general varieties of polynomial growth.It turns out that for $k\,\le \,4$ there are only a finite number of varieties of polynomial growth ${{n}^{k}}$ , but for each $k\,>\,4$ , the number of minimal varieties is at least $\left| F \right|$ , the cardinality of the base field, and we give a recipe for their construction.
DOI : 10.4153/CJM-2013-016-5
Mots-clés : 16R10, 16P90, polynomial identity, codimension, polynomial growth, T-ideal 
Giambruno, Antonio; Mattina, Daniela La; Zaicev, Mikhail. Classifying the Minimal Varieties of Polynomial Growth. Canadian journal of mathematics, Tome 66 (2014) no. 3, pp. 625-640. doi: 10.4153/CJM-2013-016-5
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     title = {Classifying the {Minimal} {Varieties} of {Polynomial} {Growth}},
     journal = {Canadian journal of mathematics},
     pages = {625--640},
     year = {2014},
     volume = {66},
     number = {3},
     doi = {10.4153/CJM-2013-016-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2013-016-5/}
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