Maximal subalgebras of Cartan type in the exceptional Lie algebras

Sebastian Herpel ^[2] ; David I. Stewart ^[1]
1. [1] University of Cambridge
  
  University of Cambridge
  
  Cambridge District, Reino Unido
2. [2] Ruhr Universität Bochum
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 22, Nº. 2, 2016, págs. 765-799
Idioma: inglés
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Resumen
- In this paper, we initiate the study of the maximal subalgebras of exceptional simple classical Lie algebras gg over algebraically closed fields k of positive characteristic p, such that the prime characteristic is good for gg . We deal with what is surely the most unnatural case; that is, where the maximal subalgebra in question is a simple subalgebra of non-classical type. We show that only the first Witt algebra can occur as a subalgebra of gg and give an explicit classification of when it is maximal in gg .