# Codimensions of algebras and growth functions

Antonino Giambruno, Mikhail Zaicev, Giambruno, Sergey Mishchenko

Risultato della ricerca: Articlepeer review

51 Citazioni (Scopus)

## Abstract

Let $A$ be an algebra over a field $F$ of characteristic zero and let $c_n(A),\ n=1,2,\ldots,$ be its sequence of codimensions. We prove that if $c_n(A)$ is exponentially bounded, its exponential growth can be any realnumber $>1$. This is achieved by constructing, for any real number $\alpha >1$, an $F$-algebra $A_\alpha$ such that $\lim_{n\to \infty} \root n \of {c_n(A_\alpha)}$ exists and equals $\alpha$. The methods are based on the representation theory of the symmetric group and on properties of infinite Sturmian and periodic words.
Lingua originale English 1027-1052 Advances in Mathematics 217 Published - 2008

## All Science Journal Classification (ASJC) codes

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