𝔖 Bobbio Scriptorium
✦   LIBER   ✦

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

No coin nor oath required. For personal study only.

✦ 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 .


📜 SIMILAR VOLUMES


Jordan–Lie Super Algebra and Jordan–Lie
✍ Susumu Okubo; Noriaki Kamiya 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 269 KB

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.

Primitivity in Jordan Systems is Ubiquit
✍ José A. Anquela; Teresa Cortés 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 232 KB

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-side

Jordan Triples and Operads
✍ Allahtan Victor Gnedbaye; Marc Wambst 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 114 KB

We study the Jordan triple systems in terms of operads. We give the description of the operad of these ternary algebras as a quadratic operad and prove that the quadratic dual of this operad is the operad of partially antisymmetric, partially associative ternary algebras. Nous étudions les systèmes

Jordan Pairs and Hopf Algebras
✍ John R Faulkner 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 273 KB

A quadratic Jordan pair is constructed from a ‫-ޚ‬graded Hopf algebra having divided power sequences over all primitive elements and with three terms in the ‫-ޚ‬grading of the primitive elements. The notion of a divided power representation of a Jordan pair is introduced and the universal object is

Identities for Generalized Lie and Jorda
✍ Murray Bremner; Irvin Hentzel 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 110 KB

We determine the identities of degree F 9 satisfied by the new ternary opera-Ž . tions abc q bca q cab q acb q bac q cba symmetric sum , abc q bca q cab y Ž . Ž . acb y bac y cba alternating sum , and abc q bca q cab cyclic sum on every Ž . Ž . triple system satisfying the total associativity identi

Grids and the Arithmetics of Jordan Pair
✍ Holger P. Petersson 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 338 KB

We prove that every 2-finitedimensional covering standard division grid of a Jordan pair V over a Henselian field canonically determines a norm on V. This is used to classify maximal orders which contain a covering division grid of V. We show that weakly separable orders always satisfy this conditio