vi CONTENTS
Chapter 3. The Contragredient Case 69
3.1. Introduction 69
3.2. Results on modules for three-dimensional Lie algebras 69
3.3. Primitive vectors in g1 and g−1 74
3.4. Subalgebras with a balanced grading 77
3.5. Algebras with an unbalanced grading 86
Chapter 4. The Noncontragredient Case 97
4.1. General assumptions and notation 97
4.2. Brackets of weight vectors in opposite gradation spaces 98
4.3. Determining g0 and its representation on g−1 99
4.4. Additional assumptions 105
4.5. Computing weights of
b−-primitive
vectors in g1 105
4.6. Determination of the local Lie algebra 115
4.7. The irreducibility of g1 125
4.8. Determining the negative part when g1 is irreducible 133
4.9. Determining the negative part when g1 is reducible 137
4.10. The case that g0 is abelian 141
4.11. Completion of the proof of the Main Theorem 142
Bibliography 143
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