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- Title
Affine varieties and lie algebras of vector fields.
- Authors
Hauser, Herwig; Müller, Gerd
- Abstract
In this article, we associate to affine algebraic or local analytic varieties their tangent algebra. This is the Lie algebra of all vector fields on the ambient space which are tangent to the variety. Properties of the relation between varieties and tangent algebras are studied. Being the tangent algebra of some variety is shown to be equivalent to a purely Lie algebra theoretic property of subalgebras of the Lie algebra of all vector fields on the ambient space. This allows to prove that the isomorphism type of the variety is determinde by its tangent algebra.
- Publication
Manuscripta Mathematica, 1993, Vol 80, Issue 1, p309
- ISSN
0025-2611
- Publication type
Article
- DOI
10.1007/BF03026556