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Varieties of almost polynomial growth: classifying their subvarieties

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Let G be the infinite dimensional Grassmann algebra over a field F of characteristic zero and UT 2 the algebra of 2 × 2 upper triangular matrices over F. The relevance of these algebras in PI-theory relies on the fact that they generate the only two varieties of almost polynomial growth, i.e., they grow exponentially but any proper subvariety grows polynomially. In this paper we completely classify, up to PI-equivalence, the associative algebras A such that A ∈ Var(G) or A ∈ Var(UT 2).

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  1. Dipartimento di Matematica e Applicazioni, Via Archirafi 34, 90123, Palermo, Italy

    Daniela La Mattina

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  1. Daniela La Mattina
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La Mattina, D. Varieties of almost polynomial growth: classifying their subvarieties. manuscripta math. 123, 185–203 (2007). https://doi.org/10.1007/s00229-007-0091-5

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  • DOI: https://doi.org/10.1007/s00229-007-0091-5

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