Analytic varieties versus integral varieties of Lie algebras of vector fields
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- by Herwig Hauser and Gerd Müller PDF
- Bull. Amer. Math. Soc. 26 (1992), 276-279 Request permission
Abstract:
We associate to any germ of an analytic variety a Lie algebra of tangent vector fields, the tangent algebra. Conversely, to any Lie algebra of vector fields an analytic germ can be associated, the 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.References
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H. Hauser and G. Müller, Analytic varieties and Lie algebras of vector fields. Part I: The Gröbner correspondence, preprint 1991. To be published.
—, Analytic varieties and Lie algebras of vector fields. Part II: Singularities are determined by their tangent algebra (to appear).
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 26 (1992), 276-279
- MSC (2000): Primary 32B10; Secondary 17B40
- DOI: https://doi.org/10.1090/S0273-0979-1992-00272-0
- MathSciNet review: 1121570