Please use this identifier to cite or link to this item:
Title: The non-projective part of the Lie module for the symmetric group
Authors: Erdmann, K.
Tan, K.M. 
Keywords: Block component
Free Lie algebra
Lie module
Schur algebra
Symmetric group
Issue Date: Jun-2011
Citation: Erdmann, K., Tan, K.M. (2011-06). The non-projective part of the Lie module for the symmetric group. Archiv der Mathematik 96 (6) : 513-518. ScholarBank@NUS Repository.
Abstract: The Lie module of the group algebra of the symmetric group is known to be not projective if and only if the characteristic p of F divides n. We show that in this case its non-projective summands belong to the principal block of. Let V be a vector space of dimension m over F, and let Ln(V) be the n-th homogeneous part of the free Lie algebra on V; this is a polynomial representation of GLm(F) of degree n, or equivalently, a module of the Schur algebra S(m, n). Our result implies that, when m ≥ n, every summand of Ln(V) which is not a tilting module belongs to the principal block of S(m, n), by which we mean the block containing the n-th symmetric power of V. © 2011 Springer Basel AG.
Source Title: Archiv der Mathematik
ISSN: 0003889X
DOI: 10.1007/s00013-011-0269-7
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.


checked on Aug 6, 2020


checked on Jul 29, 2020

Page view(s)

checked on Aug 1, 2020

Google ScholarTM



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.