Analytic varieties versus integral varieties of Lie algebras of vector fields
Complex Variables
2016-09-06 v1
Abstract
We associate to any germ of an analytic variety a Lie algebra of tangent vector fields, the {\it tangent algebra}. Conversely, to any Lie algebra of vector fields an analytic germ can be associated, the {\it integral variety}. The paper investigates properties of this correspondence: The set of all tangent algebras is characterized in purely Lie algebra theoretic terms. And it is shown that the tangent algebra determines the analytic type of the variety.
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Cite
@article{arxiv.math/9204232,
title = {Analytic varieties versus integral varieties of Lie algebras of vector fields},
author = {Herwig Hauser and Gerd Muller},
journal= {arXiv preprint arXiv:math/9204232},
year = {2016}
}
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4 pages