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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

Analytic varieties versus integral varieties of Lie algebras of vector fields


Authors: Herwig Hauser and Gerd Müller
Journal: Bull. Amer. Math. Soc. 26 (1992), 276-279
MSC (2000): Primary 32B10; Secondary 17B40
MathSciNet review: 1121570
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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 [Enhancements On Off] (What's this?)

  • [HM1] H. Hauser and G. Müller, Analytic varieties and Lie algebras of vector fields. Part I: The Gröbner correspondence, preprint 1991. To be published.
  • [HM2] -, Analytic varieties and Lie algebras of vector fields. Part II: Singularities are determined by their tangent algebra (to appear).
  • [N] Raghavan Narasimhan, Analysis on real and complex manifolds, Advanced Studies in Pure Mathematics, Vol. 1, Masson & Cie, Éditeurs, Paris; North-Holland Publishing Co., Amsterdam, 1968. MR 0251745 (40 #4972)
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Additional Information

DOI: http://dx.doi.org/10.1090/S0273-0979-1992-00272-0
PII: S 0273-0979(1992)00272-0
Article copyright: © Copyright 1992 American Mathematical Society