# The Automorphism Group of the Free Algebra of Rank Two

Serdica Mathematical Journal (2002)

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

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topCohn, 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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