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Metabelian Lie powers of the natural module for a general linear group

Erdmann, Karin; Kovacs, L


Consider a free metabelian Lie algebra M of finite rank r over an infinite field K of prime characteristic p. Given a free generating set, M acquires a grading; its group of graded automorphisms is the general linear group GLr(K), so each homogeneous component Md is a finite dimensional GLr(K)-module. The homogeneous component M1 of degree 1 is the natural module, and the other Md are the metabelian Lie powers of the title.This paper investigates the submodule structure of the Md. In the main...[Show more]

CollectionsANU Research Publications
Date published: 2011
Type: Journal article
Source: Journal of Algebra
DOI: 10.1016/j.jalgebra.2011.11.021


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