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Gelfand–Kirillov Dimension for Automorphism Groups of Relatively Free Algebras

Gelfand–Kirillov Dimension for Automorphism Groups of Relatively Free Algebras Using ideas of our recent work on automorphisms of residually nilpotent relatively free groups, we introduce a new growth function for subgroups of the automorphism groups of relatively free algebras F n (V) over a field of characteristic zero and the related notion of Gelfand-Kirillov dimension, and study their behavior. We prove that, under some natural restrictions, the Gelfand-Kirillov dimension of the group of tame automorphisms of F n (V) is equal to the Gelfand-Kirillov dimension of the algebra F n (V). We show that, in some cases, the Gelfand-Kirillov dimension of the group of tame automorphisms of F n (V) is smaller than the Gelfand-Kirillov dimension of the whole automorphism group, and calculate the Gelfand-Kirillov dimension of the automorphism group of F n (V) for some important varieties V. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Algebra Colloquium Springer Journals

Gelfand–Kirillov Dimension for Automorphism Groups of Relatively Free Algebras

Drensky, V.; Papistas, A.
Algebra Colloquium , Volume 7 (3) – Jan 1, 2000
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Publisher
Springer Journals
Copyright
Copyright © 2000 by Springer-Verlag Hong Kong
Subject
Mathematics; Algebra; Algebraic Geometry
ISSN
1005-3867
eISSN
0219-1733
DOI
10.1007/s10011-000-0281-0
Publisher site
See Article on Publisher Site

Abstract

Using ideas of our recent work on automorphisms of residually nilpotent relatively free groups, we introduce a new growth function for subgroups of the automorphism groups of relatively free algebras F n (V) over a field of characteristic zero and the related notion of Gelfand-Kirillov dimension, and study their behavior. We prove that, under some natural restrictions, the Gelfand-Kirillov dimension of the group of tame automorphisms of F n (V) is equal to the Gelfand-Kirillov dimension of the algebra F n (V). We show that, in some cases, the Gelfand-Kirillov dimension of the group of tame automorphisms of F n (V) is smaller than the Gelfand-Kirillov dimension of the whole automorphism group, and calculate the Gelfand-Kirillov dimension of the automorphism group of F n (V) for some important varieties V.

Journal

Algebra Colloquium – Springer Journals

Published: Jan 1, 2000

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