Fixed Points and Stable Subgroups of Algebraic Group Automorphisms1
نویسنده
چکیده
1. Introduction. In this paper, we study the fixed point sets and stable subgroups of automorphisms of a connected algebraic linear group over an algebraically closed field of arbitrary characteristic. [7] contains a description of most of the results of this paper, and some material in [7] is essential for the present paper. Many of the results discussed in the present paper were proved at characteristic 0 by Borel-Mostow, Jacobson and Mostow (see [l], [5], [6]). In §3 it is essentially shown that if ax, a2 are ''semisimple" auto-morphisms of a connected linear algebraic group G which differ by an inner automorphism of G, and if //, is a Cartan subgroup of the connected component of the subgroup of fixed points of ai (i = l, 2), then there is an inner automorphism Int g of G such that Hx Int g = H2 and Int g_1 o ax o Int Hx o Int g = cr2 o Int H2. This is used (see §4)
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