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

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

2008-01-16

arxiv.org/abs/0801.2481v1

Mathematics

Rings and Algebras

35 pages

Scientific paper

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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