Free lie algebras as modules for symmetric groups

R. M. Bryant, L. G. Kovács, Ralph Stöhr

    Research output: Contribution to journalArticlepeer-review

    Abstract

    Let r be a positive integer, double-struck F sign a field of odd prime characteristic p, and L the free Lie algebra of rank r over double-struck F sign. Consider L a module for the symmetric group G-fraktur signr of all permutations of a free generating set of L. The homogeneous components Ln of L are finite dimensional submodules, and L is their direct sum. For p ≤ r <2p, the main results of this paper identify the non-projective indecomposable direct summands of the Ln as Specht modules or dual Specht modules corresponding to certain partitions. For the case r = p, the multiplicities of these indecomposables in the direct decompositions of the Ln are also determined, as are the multiplicities of the projective indecomposables. (Corresponding results for p = 2 have been obtained elsewhere.).
    Original languageEnglish
    Pages (from-to)143-156
    Number of pages13
    JournalAustralian Mathematical Society. Journal
    Volume67
    Issue number2
    Publication statusPublished - Oct 1999

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