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arXiv · 0801.2481

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

Alberto Elduque·Susumu Okubo
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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 case of S3-symmetry, the Lie algebras are coordinatized by some nonassociative systems, which are termed generalized Malcev algebras, as they extend the classical Malcev algebras. These systems are endowed with a binary and a ternary products, and include both the Malcev algebras and the Jordan triple systems.

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Alberto Elduque, Susumu Okubo. 2008-01-16. Lie algebras with S3 or S4-action, and generalized Malcev algebras. https://arxiv.org/abs/0801.2481

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