Exceptional Lie groups, Ichiro Yokota (original) (raw)

In the end of 19 century, W. Killing and E. Cartan classified the complex simple Lie algebras, called A n , B n , C n , D n (classical type) and G 2 , F 4 , E 6 , E 7 , E 8 (exceptional type). These simple Lie algebras and the corresponding compact simple Lie groups have offered many subjects in mathematicians. Especially, exceptional Lie groups are very wonderful and interesting miracle in Lie group theory. Now, in the present book, we describe simply connected compact exceptional simple Lie groups G 2 , F 4 , E 6 , E 7 , E 8 , in very elementary way. The contents are given as follows. We first construct all simply connected compact exceptional Lie groups G concretely. Next, we find all involutive automorphisms σ of G, and determine the group structures of the fixed points subgroup G σ by σ. Note that they correspond to classification of all irreducible compact symmetric spaces G/G σ of exceptional type, and that they also correspond to classification of all non-compact exceptional simple Lie groups. Finally, we determined the group structures of the maximal subgroups of maximal rank. At any rate, we would like this book to be used in mathematics and physics.