# 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}
}
• Published 3 October 2003
• Mathematics
• Journal of the American Mathematical Society
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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