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Title: The Automorphism Group of the Free Algebra of Rank Two
Authors: Cohn, P.
Keywords: Free Algebra
Free Product with Amalgamation
Affine Automorphism
Linear Automorphism
Bipolar Structure
Issue Date: 2002
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 28, No 3, (2002), 255p-266p
Abstract: The theorem of Czerniakiewicz and Makar-Limanov, that all the automorphisms of a free algebra of rank two are tame is proved here by showing that the group of these automorphisms is the free product of two groups (amalgamating their intersection), the group of all affine automorphisms and the group of all triangular automorphisms. The method consists in finding a bipolar structure. As a consequence every finite subgroup of automorphisms (in characteristic zero) is shown to be conjugate to a group of linear automorphisms.
ISSN: 1310-6600
Appears in Collections:Volume 28 Number 3

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