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The automorphism group of a free group is not linear

✍ Scribed by Edward Formanek; Claudio Procesi


Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
322 KB
Volume
149
Category
Article
ISSN
0021-8693

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We show that the representations of certain automorphism groups of a free group afforded by compact Lie groups as described by Long can be decomposed into sums of trivial representations and Magnus᎐Gassner representations.

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Let F be a finitely generated free group, and let n denote its rank. A subgroup H of F is said to be automorphism-fixed, or auto-fixed for short, if there exists a set S of automorphisms of F such that H is precisely the set of elements fixed by every element of S; similarly, H is 1-auto-fixed if th