Determinants in Jordan matrix algebras

Abstract

We introduce a natural notion of determinant in matrix JB${}^{\ast }$-algebras, i.e., for hermitian matrices of biquaternions and for hermitian $3\times 3$ matrices of complex octonions. We establish several properties of these determinants which are useful to understand the structure of the Cartan factor of type $6$. As a tool we provide an explicit description of minimal projections in the Cartan factor of type $6$ and a variety of its automorphisms.

38 pages; we added one reference and one remark

References in corpus (1)

• Finite tripotents and finite JBW${}^{\ast }$-triples