I. DEFINITIONS -- II. RESTRICTED LIE ALGEBRAS -- III. THE CARTAN DECOMPOSITION -- IV. LEMMAS ON REPRESENTATIONS AND THEIR APPLICATIONS -- V. WEIGHTS AND ROOTS -- VI. SIMPLE SYSTEMS OF ROOTS -- VII. EXISTENCE OF SIMPLE SYSTEMS -- VIII. SYSTEMS OF TYPE A -- IX. SYSTEMS OF TYPE D -- X. SYSTEMS OF TYPE B -- XI. SYSTEMS OF TYPE C -- XII. SYSTEMS OF TYPE G -- XIII. SYSTEMS OF TYPE F -- XIV. SYSTEMS OF TYPE E -- XV. MAXIMAL SIMPLE SYSTEMS -- XVI. CLASSIFICATION OF THE SIMPLE ALGEBRAS -- XVII. THE CLASSICAL SIMPLE ALGEBRAS -- XVIII. THE FIVE EXCEPTIONAL ALGEBRAS
Notes
This paper is essentially the author's doctoral dissertation at Yale University
