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Dense Subgroups of the Automorphism Groups of Free Algebras

Published online by Cambridge University Press:  20 November 2018

Roger M. Bryant
Department of Mathematics University of Manchester Institute of Science and Technology Manchester, M60 1QD United Kingdom
Vesselin Drensky
Institute of Mathematics Bulgarian Academy of Sciences Sofia Bulgaria
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Let F be the free metabelian Lie algebra of finite rank m over a field K of characteristic 0. The automorphism group Aut F is considered with respect to a topology called the formal power series topology and it is shown that the group of tame automorphisms (automorphisms induced from the free Lie algebra of rank m) is dense in Aut F for m ≥ 4 but not dense for m = 2 and m = 3. At a more general level, we study the formal power series topology on the semigroup of all endomorphisms of an arbitrary (associative or non-associative) relatively free algebra of finite rank m and investigate certain associated modules of the general linear group GLm(AT).

Research Article
Copyright © Canadian Mathematical Society 1993


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