Polynomial identities for jordan pairs

Abstract

Varieties of Jordan pairs are considered in the present paper. The main results obtained are the following.1. The special Jordan pairs do not form a variety. More precisely, we give an example of a special Jordan pair and its homomorphic image being not special. 2. The varieties of Jordan pairs var (M_n,M_n) and var (H_n,H_n) are not special when n > 3 for M_n and H_n being n x n matrices and symmetric matrices, respectively. 3. Some description of the representations of the pair (H_n,H_n) is obtained