Completion of the Classification (eBook)

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Helmut Strade, University of Hamburg, Germany.

Introduction 9
16 Miscellaneous 11
16.1 Tori in some simple Lie algebras 11
16.2 Maximal tori in H(2 1
16.3 Representations of H(2 1
16.3.1 Central Extensions 25
16.3.2 Representations of dimension = p2 27
16.3.3 Splitting off the radical 39
16.4 Some properties of Melikian algebras 46
17 Sections 56
17.1 On trigonalizability 56
17.2 1-sections in simple Lie algebras of absolute toral rank 2 69
17.3 On the [p]-nilpotency of elements 81
17.4 2-sections 91
18 Solving the case when T is non-standard 103
18.1 2-sections revisited 103
18.2 Melikian pairs 115
18.3 Conclusion 119
19 Solving the case when all T-roots are solvable 129
19.1 2-sections revisited 129
19.2 The case when TR(L) = 3 131
19.3 Solvable sections 150
19.4 Conclusion 160
20 Attacking the general case 175
20.1 Optimal tori 176
20.2 Root spaces in 2-sections 186
20.3 The distinguished subalgebra Q(L,T) 193
20.4 Pushing the classical case 199
20.5 The filtration defined by Q(L,T) 203
20.6 Determining G(L,T) 211
20.7 Completing the classification 229
20.8 Epilogue 245
Notation 247
Bibliography 249

lt;P>"The book under review will surely become a primary source of reference on simple Lie algebras of positive characteristic. Its publication makes the achievements in this field accessible to a large group of mathematicians." Mathematical Reviews

"In conclusion, this book together with the two previous volumes will be very useful for researchers in modular Lie theory [...]." Zentralblatt für Mathematik