Codimension growth of special simple Jordan algebras

Antonino Giambruno, Mikhail Zaicev

Risultato della ricerca: Article

24 Citazioni (Scopus)

Abstract

Let $R$ be a special simple Jordan algebra over a field of characteristic zero. We exhibit a noncommutative Jordan polynomial $f$ multialternating on disjoint sets of variables which is not a polynomial identity of $R$. We then study the growth of the polynomial identities of the Jordan algebra $R$ through an analysis of its sequence of Jordan codimensions. By exploiting the basic properties of the polynomials $f$, we are able to compute the exponential rate of growth of the sequence of Jordan codimensions of $R$ and prove that it equals the dimension of the Jordan algebra over its center. We also show that for any finite dimensional special Jordan algebra, such exponential rate of growth cannot be strictly between $1$ and $2$.
Lingua originaleEnglish
pagine (da-a)3107-3123
Numero di pagine17
RivistaTransactions of the American Mathematical Society
Volume362
Stato di pubblicazionePublished - 2010

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Entra nei temi di ricerca di 'Codimension growth of special simple Jordan algebras'. Insieme formano una fingerprint unica.

  • Cita questo