In this paper we give a characterization of primitivity of Jordan pairs and triple systems in terms of their local algebras. As a consequence of that local characterization we extend to Jordan pairs and triple systems most of the known results about primitive Jordan algebras. In particular, we descr
Primitivity in Jordan Systems is Ubiquitous
✍ Scribed by José A. Anquela; Teresa Cortés
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 232 KB
- Volume
- 202
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
Ž q y . The main result of the paper asserts that if a Jordan pair
X .
-primitive at some 0 / b g V , then it is " -primitive at any 0 / b g V . Also, if a Jordan triple system T is primitive at some 0 / b g T, then it is primitive at any 0 / b X g T. As a tool, similar results concerning one-sided primitivity and
)-primitivity of associative pairs and triple systems are established. Equivalences between our definitions of primitivity and some other appearing in the literature are also obtained as a consequence.
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