Analytic varieties versus integral varieties of Lie algebras of vector fields

Herwig Hauser; Gerd Muller

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Analytic varieties versus integral varieties of Lie algebras of vector fields

Herwig Hauser·Gerd Muller

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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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BibTeX RIS

Herwig Hauser, Gerd Muller. 1992-04-01. Analytic varieties versus integral varieties of Lie algebras of vector fields. https://arxiv.org/abs/math/9204232

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