The Automorphism Group of the Free Algebra of Rank Two

Cohn, P.

Serdica Mathematical Journal (2002)

  • Volume: 28, Issue: 3, page 255-266
  • ISSN: 1310-6600

Abstract

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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.

How to cite

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Cohn, P.. "The Automorphism Group of the Free Algebra of Rank Two." Serdica Mathematical Journal 28.3 (2002): 255-266. <http://eudml.org/doc/11561>.

@article{Cohn2002,
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.},
author = {Cohn, P.},
journal = {Serdica Mathematical Journal},
keywords = {Free Algebra; Free Product with Amalgamation; Affine Automorphism; Linear Automorphism; Bipolar Structure; free algebras; free products with amalgamation; affine automorphisms; linear automorphisms; bipolar structures; tame automorphisms; automorphism groups},
language = {eng},
number = {3},
pages = {255-266},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {The Automorphism Group of the Free Algebra of Rank Two},
url = {http://eudml.org/doc/11561},
volume = {28},
year = {2002},
}

TY - JOUR
AU - Cohn, P.
TI - The Automorphism Group of the Free Algebra of Rank Two
JO - Serdica Mathematical Journal
PY - 2002
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 28
IS - 3
SP - 255
EP - 266
AB - 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.
LA - eng
KW - Free Algebra; Free Product with Amalgamation; Affine Automorphism; Linear Automorphism; Bipolar Structure; free algebras; free products with amalgamation; affine automorphisms; linear automorphisms; bipolar structures; tame automorphisms; automorphism groups
UR - http://eudml.org/doc/11561
ER -

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