Varieties of Algebras of Polynomial Growth

Daniela La Mattina

Bollettino dell'Unione Matematica Italiana (2008)

  • Volume: 1, Issue: 3, page 525-538
  • ISSN: 0392-4041

Abstract

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Let 𝒱 be a proper variety of associative algebras over a field F of characteristic zero. It is well-known that 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 𝐯𝐚𝐫 ⁡ ( G ) and 𝐯𝐚𝐫 ⁡ ( U ⁢ T 2 ) , where G is the Grassmann algebra and U ⁢ T 2 is the algebra of 2 × 2 upper triangular matrices.

How to cite

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La Mattina, Daniela. "Varieties of Algebras of Polynomial Growth." Bollettino dell'Unione Matematica Italiana 1.3 (2008): 525-538. <http://eudml.org/doc/290465>.

@article{LaMattina2008,
abstract = {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.},
author = {La Mattina, Daniela},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {525-538},
publisher = {Unione Matematica Italiana},
title = {Varieties of Algebras of Polynomial Growth},
url = {http://eudml.org/doc/290465},
volume = {1},
year = {2008},
}

TY - JOUR
AU - La Mattina, Daniela
TI - Varieties of Algebras of Polynomial Growth
JO - Bollettino dell'Unione Matematica Italiana
DA - 2008/10//
PB - Unione Matematica Italiana
VL - 1
IS - 3
SP - 525
EP - 538
AB - 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.
LA - eng
UR - http://eudml.org/doc/290465
ER -

References

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