Automorphisms of the Lie algebra of vector fields on affine -space
Hanspeter Kraft
Universität Basel, SwitzerlandAndriy Regeta
Université de Grenoble I, France
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Abstract
We study the vector fields Vec on affine -space , the subspace Vec of vector fields with constant divergence, and the subspace Vec of vector fields with divergence zero, and we show that their automorphisms, as Lie algebras, are induced by the automorphisms of :
This generalizes results of the second author obtained in dimension 2, see [Reg13]. The case of Vec goes back to Kulikov [Kul92]. This generalization is crucial in the context of infinite-dimensional algebraic groups, because Vec is canonically isomorphic to the Lie algebra of Aut, and Vec is isomorphic to the Lie algebra of the closed subgroup SAut Aut of automorphisms with Jacobian determinant equal to 1.
Cite this article
Hanspeter Kraft, Andriy Regeta, Automorphisms of the Lie algebra of vector fields on affine -space. J. Eur. Math. Soc. 19 (2017), no. 5, pp. 1577–1588
DOI 10.4171/JEMS/700