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arXiv · 2110.10458

Determinants in Jordan matrix algebras

Jan Hamhalter·Ondřej F. K. Kalenda·Antonio M. Peralta
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Abstract

We introduce a natural notion of determinant in matrix JB$^*$-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.

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Jan Hamhalter, Ondřej F. K. Kalenda, Antonio M. Peralta. 2021-10-20. Determinants in Jordan matrix algebras. https://doi.org/10.1080/03081087.2022.2049187

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