Locally finite sets of derivations

Michael Chitayat; Daniel Daigle; Andriy Regeta

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arXiv · 2606.08677

Locally finite sets of derivations

Michael Chitayat·Daniel Daigle·Andriy Regeta

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Abstract

Given an algebra B over a field k, we study conditions under which a Lie subalgebra of Der(B) is locally finite as a set of derivations. As an application of our results, we show that if X is a quasi-affine variety over an arbitrary field k, and if L is a finitely generated solvable Lie subalgebra of Der O(X) consisting of locally finite derivations, then L is locally finite. If, moreover, k is algebraically closed and of characteristic zero, and X is irreducible and affine, then L is integrable.

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Michael Chitayat, Daniel Daigle, Andriy Regeta. 2026-06-07. Locally finite sets of derivations. https://arxiv.org/abs/2606.08677

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