Triangle Equations and Simple Lie Algebras

PART I: Properties of Nondegenerate Solutions
1. Elliptic Solutions 2. Brief Survey of Semisimple Lie Algebras 3. The Simplest Trigonometric Solutions 4.
Modified Triangle Equation for Constants 5. Trigonometric Solutions (General Case) 6. Rational Solutions Having No Poles at Infinity
PART II: Automorphisms of Simple Lie Algebras
1. Equivalence of the Three Definitions of Nondegeneracy 2. Myrberg's Theorem and the General Classification of Solutions 3. Modified Triangle Equation for Constants (Conclusion) 4. Trigonometric Solutions (Conclusion)