NONCOMMUTATIVE MATRIX JORDAN ALGEBRAS, CAYLEY-DICKSON ALGEBRAS, AND SCHAFERS THEOREM

Authors
BROWN RB HOPKINS NC
Citation
Rb. Brown et Nc. Hopkins, NONCOMMUTATIVE MATRIX JORDAN ALGEBRAS, CAYLEY-DICKSON ALGEBRAS, AND SCHAFERS THEOREM, Communications in algebra, 23(1), 1995, pp. 373-397
Citations number
15
Categorie Soggetti
Mathematics, Pure",Mathematics
Journal title
Communications in algebra → ACNP
ISSN journal
00927872
Volume
23
Issue
1
Year of publication
1995
Pages
373 - 397
Database
ISI
SICI code
0092-7872(1995)23:1<373:NMJACA>2.0.ZU;2-P
Abstract
We provide a construction of noncommutative Jordan algebras of degree two. The construction can be iterated, and pre show that after the fir st few iterations no new derivations arise. The relationship between t his iterative process and the Cayley-Dickson process is studied, and t he result on derivations is used to obtain a generalization of Schafer 's classical theorem on the derivation algebras of Cayley-Dickson alge bras.