Codimension growth of special simple Jordan algebras

Antonino Giambruno, Mikhail Zaicev

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


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 $2$.
Original languageEnglish
Pages (from-to)3107-3123
Number of pages17
JournalTransactions of the American Mathematical Society
Publication statusPublished - 2010

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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