# The tame and the wild automorphisms of polynomial rings in three variables

@article{Shestakov2003TheTA, title={The tame and the wild automorphisms of polynomial rings in three variables}, author={Ivan P. Shestakov and Ualbai U. Umirbaev}, journal={Journal of the American Mathematical Society}, year={2003}, volume={17}, pages={197-227} }

Let C = F [x1, x2, . . . , xn] be the polynomial ring in the variables x1, x2, . . . , xn over a field F , and let AutC be the group of automorphisms of C as an algebra over F . An automorphism τ ∈ AutC is called elementary if it has a form τ : (x1, . . . , xi−1, xi, xi+1, . . . , xn) 7→ (x1, . . . , xi−1, αxi + f, xi+1, . . . , xn), where 0 6= α ∈ F, f ∈ F [x1, . . . , xi−1, xi+1, . . . , xn]. The subgroup of AutC generated by all the elementary automorphisms is called the tame subgroup, and…

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