Please use this identifier to cite or link to this item: https://doi.org/10.1093/qmath/har027
Title: Asymptotic behaviour of Lie powers and Lie modules
Authors: Bryant, R.M.
Lim, K.J. 
Tan, K.M. 
Issue Date: Dec-2012
Citation: Bryant, R.M., Lim, K.J., Tan, K.M. (2012-12). Asymptotic behaviour of Lie powers and Lie modules. Quarterly Journal of Mathematics 63 (4) : 845-853. ScholarBank@NUS Repository. https://doi.org/10.1093/qmath/har027
Abstract: Let V be a finite-dimensional FG-module, where F is a field of prime characteristic p and G is a group. We show that, when r is not a power of p, the Lie power L r(V) has a direct summand B r(V), which is a direct summand of the tensor power V ⊗r such that dim B r (V)/ dim L r (V) → 1 as r→∞. Similarly, for the same values of r, we obtain a projective submodule C(r) of the Lie module Lie (r) over F such that dim C(r)/dim Lie (r)→1 as r→∞. © 2011. Published by Oxford University Press. All rights reserved.
Source Title: Quarterly Journal of Mathematics
URI: http://scholarbank.nus.edu.sg/handle/10635/102892
ISSN: 00335606
DOI: 10.1093/qmath/har027
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