Proper identities, Lie identities and exponential codimension growth

Antonino Giambruno, Mikhail Zaicev

Risultato della ricerca: Articlepeer review

12 Citazioni (Scopus)

Abstract

The exponent $\mbox{exp}(A)$ of a PI-algebra $A$ in characteristic zero is an integer measuring the exponential rate of growth of the sequence of codimensions of $A$ (\cite{gz1,gz2}). In this paper we study the exponential rate of growth of the sequences of proper codimensions and Lie codimensions of an associative PI-algebra. We prove that the corresponding proper exponent exists for all PI-algebras, except for some algebras of exponent two strictly related to the Grassmann algebra. We also prove that the Lie exponent exists for any finitely generated PI-algebra. The value of both exponents is always equal to $\mbox{exp}(A)$ or $\mbox{exp}(A)-1$.
Lingua originaleEnglish
pagine (da-a)1933-1962
Numero di pagine29
RivistaJournal of Algebra
Volume320
Stato di pubblicazionePublished - 2008

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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