The structure of connected solvable groups is made clear enough by the results of the preceding chapter. What is still lacking is insight into the interaction between an arbitrary algebraic group and its subgroups of this type. Borel’s fixed point theorem (21.2) provides this insight. Here, for the first time, we make essential use of homogeneous spaces G/H which are projective (or complete) varieties. G will denote an arbitrary algebraic group, assumed from (21.3) on to be connected.
KeywordsAlgebraic Group Projective Variety Parabolic Subgroup Maximal Torus Closed Subgroup
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