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.
