Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-26T17:17:47.107Z Has data issue: false hasContentIssue false
  • English
  • Français

Lie algebras with S3- or S4-action and generalized Malcev algebras

Published online by Cambridge University Press:  25 March 2009

Alberto Elduque  and
Susumu Okubo
Alberto Elduque
Affiliation:
Departamento de Matemáticas e Instituto Universitario de Matemáticas y Aplicaciones, Universidad de Zaragoza, 50009 Zaragoza, Spain (elduque@unizar.es)
Susumu Okubo
Affiliation:
Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA (okubo@pas.rochester.edu)
Get access Rights & Permissions [Opens in a new window]

Abstract

Lie algebras endowed with an action by automorphisms of any of the symmetric groups S3 or S4 are considered, and their decomposition into a direct sum of irreducible modules for the given action is studied. In the case of S3-symmetry, the Lie algebras are coordinatized by some non-associative systems, which are termed generalized Malcev algebras, as they extend the classical Malcev algebras. These systems are endowed with a binary and a ternary product, and include both the Malcev algebras and the Jordan triple systems.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 2 , April 2009 , pp. 321 - 357
Copyright
Copyright © Royal Society of Edinburgh 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)