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Abstract
In this paper, we first give some properties of automorphisms of affine Kac-Moody algebras. Then we present a classification of order three automorphisms. An explicit, complete and non-redundant set of conjugacy classes of order 3 automorphisms is given and the fixed point sets are computed for each conjugacy class. Finally we study finite order inner automorphisms of the first kind. For a positive integer m, we identify the order m automorphisms with sequences of non-negative integers and give an explicit classification. As a consequence, we list the conjugacy classes of lower order automorphisms.
ACKNOWLEDGMENTS
Project supported by the National Natural Science Foundation of China (grant No.19901015), China Postdoctoral Science Foundation, K.C. Wong Education Foundation, Hong Kong and the Natural Science Foundation of Hebei Province.