Abstract
In this paper we show that the Koecher's Jordan automorphic generators of one variable on an irreducible symmetric cone are enough to determine the elements of scalar multiple of the Jordan identity on the attached simple Euclidean Jordan algebra. Its various geometric, Jordan and Lie theoretic interpretations associated to the Cartan-Hadamard metric and Cartan decomposition of the linear automorphisms group of a symmetric cone are given with validity on infinite-dimensional spin factors.
| Original language | English |
|---|---|
| Pages (from-to) | 507-528 |
| Number of pages | 22 |
| Journal | Journal of the Korean Mathematical Society |
| Volume | 43 |
| Issue number | 3 |
| DOIs | |
| State | Published - May 2006 |
| Externally published | Yes |
Keywords
- Cartan decomposition
- Euclidean Jordan algebra
- Global tubular neighborhood theorem
- Jordan automorphism
- Koecher's theorem
- Metric and spectral geometric mean
- Simultaneous diagonalization
- Spin factor
- Symmetric cone
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