TY - JOUR

T1 - Free lie algebras as modules for symmetric groups

AU - Bryant, R. M.

AU - Kovács, L. G.

AU - Stöhr, Ralph

PY - 1999/10

Y1 - 1999/10

N2 - 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.).

AB - 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.).

UR - http://www.scopus.com/inward/record.url?scp=0039251409&partnerID=8YFLogxK

U2 - 10.1017/s1446788700001130

DO - 10.1017/s1446788700001130

M3 - Article

SN - 1446-7887

VL - 67

SP - 143

EP - 156

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

IS - 2

ER -