Linear Representations of the Automorphism Group of a Free Group

Details Linear Representations of the Automorphism Group of a Free Group Linear Representations of the Automorphism Group of a Free Group

2006-06-08

arxiv.org/abs/math/0606182v1

Mathematics

Group Theory

Scientific paper

Let $F_n$ be the free group on $n\ge 2$ elements and $\A(F_n)$ its group of automorphisms. In this paper we present a rich collection of linear representations of $\A(F_n)$ arising through the action of finite index subgroups of it on relation modules of finite quotient groups of $F_n$. We show (under certain conditions) that the images of our representations are arithmetic groups.

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