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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)
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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

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