Exponential maps of a polynomial ring in two variables

Crachiola, Anthony J.; Makar-Limanov, Leonid G.

doi:10.1007/s40863-019-00124-9

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Exponential maps of a polynomial ring in two variables

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Makar-Limanov, Leonid G.
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s40863-019-00124-9
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Citation

Crachiola, A. J., & Makar-Limanov, L. G. (2019). Exponential maps of a polynomial ring in two variables. São Paulo Journal of Mathematical Sciences, 13(1), 73-82. doi:10.1007/s40863-019-00124-9.

Cite as: https://hdl.handle.net/21.11116/0000-0004-6998-B

Abstract

Let k be a field. We show that the ring of invariants of every exponential map on k[x,y] is generated by the image of x or y under a composition of triangular automorphisms. From this we obtain two well-known theorems on k[x,y] with no restriction on the characteristic of k: the Rentschler–Miyanishi theorem and the Jung–van der Kulk
theorem.