Triangular 𝐺ₐ actions on 𝐂⁴

Deveney, James; Finston, David; van Rossum, Peter

doi:10.1090/S0002-9939-04-07500-8

Triangular $G_{a}$ actions on $\mathbf {C}^{4}$
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by James K. Deveney, David R. Finston and Peter van Rossum PDF

Proc. Amer. Math. Soc. 132 (2004), 2841-2848 Request permission

Abstract:

Every locally trivial action of the additive group of complex numbers on four-dimensional complex affine space that is given by a triangular derivation is conjugate to a translation. A criterion for a proper action on complex affine $n$-space to be locally trivial is given, along with an example showing that the hypotheses of the criterion are sharp.

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