ASYMPTOTIC BEHAVIOUR OF LIE POWERS AND LIE MODULES

作者：Bryant Roger M^*; Lim Kay Jin; Tan Kai Meng

来源：The Quarterly Journal of Mathematics, 2012, 63(4): 845-853.

DOI：10.1093/qmath/har027

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-circle times r such that dim B-r (V)/ dim L-r (V) -> 1 as r ->infinity. 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 ->infinity.

• 出版日期2012-12