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Abstract:
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In this paper, we classify the involutions of SL(n,k) and SO(2n+1,k), where k is the complex numbers(algebraically closed field in general), real numbers, finite field and p--adic numbers. We did this in a couple of ways: directly and by
using the charaterization given in Helminck 2000 paper. In the case of SO(2n+1,k), we restrict the classification of the involutions to theose p-adic fields where -1 is a square. We also identify those isomorphy classes whose fixed point groups are compact and prove the the others are not. The classification in this paper will be the fundamental for the analysis of other cases such SO(2n,k) and SP(n,k). |
