Functional Identities in Jordan Algebras: Associating Traces and Lie Triple Isomorphisms

Abstract

Let J be a prime nondegenerate Jordan algebra. The problem of describing the form of a symmetric biadditive map B : J × J → J satisfying (B(a, a) · b) · a = B(a, a) · (b · a) for all a, b ∈ J is discussed. As an application, Lie triple isomorphisms of Jordan algebras are considered.

Key Words:

• Jordan algebra
• Functional identities
• Associating traces
• Lie triple isomorphism

Math. Subj. Class. (2000):

• 17C10
• 17C50
• 16W10
• 16R50

Acknowledgment

The first author is supported by the Ministry of Science of Slovenia. The third author is supported by D.G.I.C.Y.T. Grant PB98-1358.