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Maximal Subgroups of Exceptional Algebraic Groups
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The goal of this book is the determination of the maximal closed connected subgroups of the simple algebraic groups of exceptional type. The main result recovers the results of Dynkin and extends them to cover the case of algebraic groups over algebraically closed fields of positive characteristic. The author first reduces to the case of semisimple subgroups, and then studies them via their action on the Lie algebra of the overlying exceptional group. The analysis is facilitated by a particular 1-dimensional torus of the subgroup which determines a labelling of the Dynkin diagram of the except...
The goal of this book is the determination of the maximal closed connected subgroups of the simple algebraic groups of exceptional type. The main result recovers the results of Dynkin and extends them to cover the case of algebraic groups over algebraically closed fields of positive characteristic. The author first reduces to the case of semisimple subgroups, and then studies them via their action on the Lie algebra of the overlying exceptional group. The analysis is facilitated by a particular 1-dimensional torus of the subgroup which determines a labelling of the Dynkin diagram of the exceptional group. The results of that paper, when combined with previous results concerning maximal subgroups of classical algebraic groups, yield a reasonably complete analysis of the maximal closed connected subgroups of simple algebraic groups.
Table of contents:
Labelled diagrams, restrictions of L(G)X, and root groups; Reduction to the case X simple; X = A1, A2, B2, G2, A3, B3, C3, A4, B4, C4, D4, F4, E6, E7; X of classical type and rank(X)55; The main theorems.
Table of contents:
Labelled diagrams, restrictions of L(G)X, and root groups; Reduction to the case X simple; X = A1, A2, B2, G2, A3, B3, C3, A4, B4, C4, D4, F4, E6, E7; X of classical type and rank(X)