Determinants in Jordan matrix algebras Hamhalter, Jan Kalenda, Ondrej F. K. Peralta Pereira, Antonio Miguel Acknowledgements The first author was supported by the project OPVVV CAAS CZ.02.1.01/0.0/0.0/16 019/0000778. Third author partially supported by MCIN / AEI / 10. 13039 / 501100011033 / FEDER “Una manera de hacer Europa” project no. PGC2018-093332-B-I00, Junta de Andalucía grants FQM375, A-FQM- 242-UGR18 and PY20 00255, and by the IMAG–María de Maeztu grant CEX2020- 001105-M / AEI / 10.13039 / 501100011033. We introduce a natural notion of determinant in matrix JB∗-algebras, i.e., for hermitian matrices of biquaternions and for hermitian 3×3 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. 2022-04-08T12:23:59Z 2022-04-08T12:23:59Z 2022-02-23 journal article Published version: Hamhalter, J., Kalenda, O. F., & Peralta, A. M. (2022). Determinants in Jordan matrix algebras. Linear and Multilinear Algebra, 1-42. [https://doi.org/10.1080/03081087.2022.2049187] http://hdl.handle.net/10481/74294 10.1080/03081087.2022.2049187 eng http://creativecommons.org/licenses/by-nc-nd/3.0/es/ open access Atribución-NoComercial-SinDerivadas 3.0 España