Geodesic
Dense Subgroups of the Automorphism Groups of Free Algebras
Canadian journal of mathematics, Tome 45 (1993) no. 6, pp. 1135-1154

Voir la notice de l'article provenant de la source Cambridge University Press

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).
DOI : 10.4153/CJM-1993-063-5
Mots-clés : 17B01, 17B30, 17B40, 17A50, 17A36 
Bryant, Roger M.; Drensky, Vesselin. Dense Subgroups of the Automorphism Groups of Free Algebras. Canadian journal of mathematics, Tome 45 (1993) no. 6, pp. 1135-1154. doi: 10.4153/CJM-1993-063-5
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