Journal of Lie Theory 32 (2022), No. 4, 1125--1138
Copyright Heldermann Verlag 2022
Primitive Lie Algebras of Rational Vector Fields
Guy Casale
Université de Rennes, CNRS, IRMAR - UMR 6625, 35000 Rennes, France
guy.casale@univ-rennes1.fr
Frank Loray
Université de Rennes, CNRS, IRMAR - UMR 6625, 35000 Rennes, France
frank.loray@univ-rennes1.fr
Jorge Vitório Pereira
IMPA, Rio de Janeiro, Brasil
jvp@impa.br
Frédéric Touzet
Université de Rennes, CNRS, IRMAR - UMR 6625, 35000 Rennes, France
frederic.touzet@univ-rennes1.fr
Let g be a transitive, finite-dimensional Lie algebra of rational vector fields on a projective manifold. If g is primitive, i.e., does not locally preserve any foliation, then it determines a rational map to an algebraic homogenous space G/H which maps g to Lie(G).
Keywords: Lie algebras of vector fields.
MSC: 16W25, 17B66, 32M25.
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