Jordan homomorphisms onto nondegenerate Jordan algebras
Let \(\phi: J_ 0\to J\) be an epimorphism of special Jordan algebras over a field of characteristic \(\neq 2\), where \(J\) is nondegenerate. The author proves that J embeds in a direct sum \(J_ 1\oplus J_ 2\) of special Jordan algebras and that \(\phi\) lifts to a direct sum \(\phi_ 1\oplus \phi_ 2\) of homomorphisms \(\phi_ i: J_ 0\to J_ i\) such that \(\phi_ 1\) lifts to a homomorphism of associative envelopes of \(J_ 0\) and \(J_ 1\) and such that \(J_ 2\) is a Wagner algebra in the sense that \([x,y]^ 2\) is central for all x and y in \(J_ 2\). Zel'manov's work plays a key role in the proof of this theorem, which generalizes a result of McCrimmon from the case where \(J\) is prime to the case where \(J\) is nondegenerate. The generalization is based on the author's work with Baxter on central closures of semiprime nonassociative algebras.
scientific article; zbMATH DE number 4163124
scientific article