Graded polynomial identities and exponential growth

Daniela La Mattina; Antonino Giambruno; Eli Aljadeff

Graded polynomial identities and exponential growth

Daniela La Mattina, Antonino Giambruno, Eli Aljadeff

Matematica e Informatica

Risultato della ricerca: Article › peer review

40 Citazioni (Scopus)

Abstract

Let $A$ be a finite dimensional algebra over a fieldof characteristic zero graded by a finite abelian group $G$. Here westudy a growth function related to the graded polynomial identitiessatisfied by $A$ by computing the exponential rate of growth of thesequence of graded codimensions of $A$. We prove that the$G$-exponent of $A$ exists and is an integer related in an explicitway to the dimension of a suitable semisimple subalgebra of $A$.

Lingua originale	English
pagine (da-a)	83-100
Numero di pagine	18
Rivista	JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK
Volume	650
Stato di pubblicazione	Published - 2011

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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title = "Graded polynomial identities and exponential growth",

abstract = "Let $A$ be a finite dimensional algebra over a fieldof characteristic zero graded by a finite abelian group $G$. Here westudy a growth function related to the graded polynomial identitiessatisfied by $A$ by computing the exponential rate of growth of thesequence of graded codimensions of $A$. We prove that the$G$-exponent of $A$ exists and is an integer related in an explicitway to the dimension of a suitable semisimple subalgebra of $A$.",

author = "{La Mattina}, Daniela and Antonino Giambruno and Eli Aljadeff",

year = "2011",

language = "English",

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T1 - Graded polynomial identities and exponential growth

AU - La Mattina, Daniela

AU - Giambruno, Antonino

AU - Aljadeff, Eli

PY - 2011

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N2 - Let $A$ be a finite dimensional algebra over a fieldof characteristic zero graded by a finite abelian group $G$. Here westudy a growth function related to the graded polynomial identitiessatisfied by $A$ by computing the exponential rate of growth of thesequence of graded codimensions of $A$. We prove that the$G$-exponent of $A$ exists and is an integer related in an explicitway to the dimension of a suitable semisimple subalgebra of $A$.

AB - Let $A$ be a finite dimensional algebra over a fieldof characteristic zero graded by a finite abelian group $G$. Here westudy a growth function related to the graded polynomial identitiessatisfied by $A$ by computing the exponential rate of growth of thesequence of graded codimensions of $A$. We prove that the$G$-exponent of $A$ exists and is an integer related in an explicitway to the dimension of a suitable semisimple subalgebra of $A$.

UR - http://hdl.handle.net/10447/97276

M3 - Article

VL - 650

SP - 83

EP - 100

JO - Journal fur die Reine und Angewandte Mathematik

JF - Journal fur die Reine und Angewandte Mathematik

SN - 0075-4102

ER -