We introduce notions of Jordan᎐Lie super algebras and Jordan᎐Lie triple systems as well as doubly graded Lie-super algebras. They are intimately related to both Lie and Jordan super algebras as well as antiassociative algebra.
Primitive Jordan Pairs and Triple Systems
✍ Scribed by José A. Anquela; Teresa Contés
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 393 KB
- Volume
- 184
- Category
- Article
- ISSN
- 0021-8693
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✦ Synopsis
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 describe primitive Jordan pairs and triple systems over an arbitrary ring of scalars in the sense of ''The Structure of Primitive Quadratic Jordan Algebras'' by J. A. Anquela, T. Cortes, and Ž .
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