Geodesic
The Automorphism Group of the Free Algebra of Rank Two
Serdica Mathematical Journal, Tome 28 (2002) no. 3, pp. 255-266.

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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.
Keywords: Free Algebra, Free Product with Amalgamation, Affine Automorphism, Linear Automorphism, Bipolar Structure 
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Cohn, P. The Automorphism Group of the Free Algebra of Rank Two. Serdica Mathematical Journal, Tome 28 (2002) no. 3, pp. 255-266. http://geodesic.mathdoc.fr/item/SMJ2_2002_28_3_a6/