𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Jordan–Lie Super Algebra and Jordan–Lie Triple System

✍ Scribed by Susumu Okubo; Noriaki Kamiya


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
269 KB
Volume
198
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis


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.


📜 SIMILAR VOLUMES


Lie Triple Systems, Restricted Lie Tripl
✍ Terrell L Hodge 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 316 KB

We define a restricted structure for Lie triple systems in the characteristic p ) 2 setting, akin to the restricted structure for Lie algebras, and initiate a study of a theory of restricted modules. In general, Lie triple systems have natural embeddings into certain canonical Lie algebras, the so-c

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

Primitive Jordan Pairs and Triple System
✍ José A. Anquela; Teresa Contés 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 393 KB

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

On Some Algebras Related to Simple Lie T
✍ Pilar Benito; Cristina Draper; Alberto Elduque 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 152 KB

Lie triple system T over a field F of characteristic zero. It turns out that it contains nontrivial elements if and only if T is related to a simple Jordan algebra. In particular this provides a new proof of the determination by Laquer of the invariant affine connections in the simply connected com

Cohomology of Dowling Lattices and Lie (
✍ Eric Gottlieb; Michelle L. Wachs 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 245 KB

We extend a well-known relationship between the representation of the symmetric group on the homology of the partition lattice and the free Lie algebra to Dowling lattices.