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 $2$.

Giambruno, A., Zaicev, M. (2010). Codimension growth of special simple Jordan algebras. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 362, 3107-3123.

Codimension growth of special simple Jordan algebras

GIAMBRUNO, Antonino;
2010-01-01

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 $2$.
Giambruno, A., Zaicev, M. (2010). Codimension growth of special simple Jordan algebras. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 362, 3107-3123.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/45118
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