Determinants in Jordan matrix algebras
Operator Algebras
2025-01-14 v2
Abstract
We introduce a natural notion of determinant in matrix JB-algebras, i.e., for hermitian matrices of biquaternions and for hermitian matrices of complex octonions. We establish several properties of these determinants which are useful to understand the structure of the Cartan factor of type . As a tool we provide an explicit description of minimal projections in the Cartan factor of type and a variety of its automorphisms.
Keywords
Cite
@article{arxiv.2110.10458,
title = {Determinants in Jordan matrix algebras},
author = {Jan Hamhalter and Ondřej F. K. Kalenda and Antonio M. Peralta},
journal= {arXiv preprint arXiv:2110.10458},
year = {2025}
}
Comments
38 pages; we added one reference and one remark