Abstract
Let p(z) ∈ ℂ[z] be a polynomial of degree at least 2. The goal is to prove the following. Suppose that ∂ is a nonzero locally nilpotent derivation (LND for short) of the ℂ-algebra R generated by x, y, and z subject to a relation xy = p(z). Then the kernel of this derivation is a polynomial ring generated by the image of x under an automorphism of R.
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References
D. Daigle, Locally nilpotent derivations of a class of two-dimensional domains, preprint.
M. Ferrero, Y. Lequain, A. Nowicki, A note on locally nilpotent derivations, J. Pure Appl. Algebra, 79 (1992), 45–50.
R. Rentschler, Operations du groupe additif sur le plane affine, C.R. Acad. Sci. Paris, 267 (1968), 384–387.
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© 2003 Springer Science+Business Media Dordrecht
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Makar-Limanov, L. (2003). Locally Nilpotent Derivations on the Surface xy = p(z). In: Proceedings of the Third International Algebra Conference. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0337-6_9
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DOI: https://doi.org/10.1007/978-94-017-0337-6_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6351-9
Online ISBN: 978-94-017-0337-6
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