New York Journal of Mathematics
Volume 19 (2013) 395-421


Laurent Bartholdi

Automorphisms of free groups. I

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Published: June 28, 2013
Keywords: Lie algebra; Automorphism groups; Lower central series
Subject: 20E36, 20F28, 20E05, 20F40

We describe, up to degree n, the Lie algebra associated with the automorphism group of a free group of rank n. We compute in particular the ranks of its homogeneous components, and their structure as modules over the linear group.

Along the way, we infirm (but confirm a weaker form of) a conjecture by Andreadakis, and answer a question by Bryant-Gupta-Levin-Mochizuki.

Author information

Mathematisches Institut, Georg-August Universität zu Göttingen, Germany