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|Title:||The non-projective part of the Lie module for the symmetric group|
Free Lie algebra
|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. https://doi.org/10.1007/s00013-011-0269-7|
|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|
|Appears in Collections:||Staff Publications|
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