Determinants in Jordan matrix algebras

Hamhalter, Jan; Kalenda, Ondrej F. K.; Peralta Pereira, Antonio Miguel

doi:10.1080/03081087.2022.2049187

PRE PRINT 2110.10458.pdf (420.8Kb)

Identificadores

URI: http://hdl.handle.net/10481/74294

DOI: 10.1080/03081087.2022.2049187

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Fecha

2022-02-23

Referencia bibliográfica

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]

Patrocinador

Project OPVVV CAAS CZ.02.1.01/0.0/0.0/16 019/0000778; 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; IMAG–María de Maeztu grant CEX2020-001105-M/AEI/10.13039/501100011033

Resumen

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.

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