Introduction ................................................... ix
16 Miscellaneous ................................................ 1
16.1 Tori in some simple Lie algebras ....................... 1
16.2 Maximal tori in H(2;1;Ф(1))[р] ......................... 5
16.3 Representations of H (2; 1; Φ(τ))(1) .................. 13
16.3.1 Central Extensions ............................ 15
16.3.2 Representations of dimension ≤ p2 ............. 17
16.3.3 Splitting off the radical ..................... 29
16.4 Some properties of Melikian algebras .................. 36
17 Sections .................................................... 46
17.1 On trigonalizability .................................. 46
17.2 1-sections in simple Lie algebras of absolute toral
rank 2 ................................................ 59
17.3 On the [p]-nilpotency of elements ..................... 71
17.4 2-sections ............................................ 81
18 Solving the case when T is non-standard ..................... 93
18.1 2-sections revisited .................................. 93
18.2 Melikian pairs ....................................... 105
18.3 Conclusion ........................................... 109
19 Solving the case when all T-roots are solvable ............. 119
19.1 2-sections revisited ................................. 119
19.2 The case when TR(L) = 3 .............................. 121
19.3 Solvable sections .................................... 140
19.4 Conclusion ........................................... 150
20 Attacking the general case ................................. 165
20.1 Optimal tori ......................................... 166
20.2 Root spaces in 2-sections ............................ 176
20.3 The distinguished subalgebra Q(L,T) .................. 183
20.4 Pushing the classical case ........................... 189
20.5 The filtration defined by Q(L,T) ..................... 193
20.6 Determining G{L,T) ................................... 201
20.7 Completing the classification ........................ 219
20.8 Epilogue ............................................. 235
Notation ...................................................... 237
Bibliography .................................................. 239
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