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arXiv · 2604.02864

Locally finite solvable Lie algebras of derivations

Mikhail Zaidenberg
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Abstract

Let X be an affine variety. The local finiteness of a Lie subalgebra h of Lie(Aut(X)) is equivalent to the existence of an algebraic subgroup G of Aut(X) such that h is contained in Lie(G). Let h be a solvable Lie subalgebra of Lie(Aut(X)) generated by a finite collection of locally finite Lie subalgebras. The authors of [arXiv:2507.09679] wondered whether h is itself locally finite. After presenting some criteria for the local finiteness of h, we answer this question in the affirmative in the particular case where X is the affine plane.

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Mikhail Zaidenberg. 2026-04-03. Locally finite solvable Lie algebras of derivations. https://arxiv.org/abs/2604.02864

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