Determinants in Jordan matrix algebras
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912183387947008 |
|---|---|
| author | Hamhalter, Jan Kalenda, Ondřej F. K. Peralta, Antonio M. |
| author_facet | Hamhalter, Jan Kalenda, Ondřej F. K. Peralta, Antonio M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_10458 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Determinants in Jordan matrix algebras Hamhalter, Jan Kalenda, Ondřej F. K. Peralta, Antonio M. Operator Algebras 46L70, 17C10, 17C40, 15A15 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. |
| title | Determinants in Jordan matrix algebras |
| topic | Operator Algebras 46L70, 17C10, 17C40, 15A15 |
| url | https://arxiv.org/abs/2110.10458 |