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A non-triangular action of $${\mathbb{G}}_ a$$ on $${\mathbb{A}}^ 3$$. (English) Zbl 0555.14019
An automorphism $$f: {\mathbb{C}}^ n\to {\mathbb{C}}^ n,$$ $$f(x)=(f_ 1(x),...,f_ n(x))$$ is ”triangular” if $$f_ i(x)$$ depends only on $$x_ 1,...,x_ i$$ $$(i=1,...,n)$$. A polynomial action of the additive group $${\mathbb{C}}$$ on $${\mathbb{C}}^ 3$$ is exhibited which cannot be conjugated, by a polynomial automorphism, into triangular form. Such examples do not exist on $${\mathbb{C}}^ 2$$.

##### MSC:
 14L30 Group actions on varieties or schemes (quotients) 32M05 Complex Lie groups, group actions on complex spaces
##### Keywords:
triangular automorphism
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##### References:
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