6533b82cfe1ef96bd128fe62

RESEARCH PRODUCT

Affine varieties and lie algebras of vector fields

Gerd MüllerGerd MüllerHerwig HauserHerwig Hauser

subject

Filtered algebraAlgebraZariski tangent spaceGeneral MathematicsAlgebra representationUniversal enveloping algebraMathematics::Differential GeometryTangent vectorAffine Lie algebraLie conformal algebraMathematicsGraded Lie algebra

description

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.

yearjournalcountryeditionlanguage
1993-12-01Manuscripta Mathematica
https://doi.org/10.1007/bf03026556