On the smoothness of normalisers, the subalgebra structure of modular Lie algebras, and the cohomology of small representations

@article{Herpel2016OnTS,
  title={On the smoothness of normalisers, the subalgebra structure of modular Lie algebras, and the cohomology of small representations},
  author={Sebastian Herpel and David I. Stewart},
  journal={Documenta Mathematica},
  year={2016}
}
We provide results on the smoothness of normalisers in connected reductive algebraic groups G over fields k of positive characteristic p. Specifically we we give bounds on p which guarantee that normalisers of subalgebras of g in G are smooth, i.e. so that the Lie algebras of these normalisers coincide with the infinitesimal normalisers. One of our main tools is to exploit cohomology vanishing of small dimensional modules. Along the way, we obtain complete reducibility results for small… 
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