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Completion of the Classification

:	Helmut Strade
:	Completion of the Classification
:	Walter de Gruyter GmbH& Co.KG
:	9783110263015
:	De Gruyter Expositions in MathematicsISSN
:	1
:	CHF 144.70
:

:	Allgemeines, Lexika
:	English

:	249
:	Wasserzeichen
:	PC/MAC/eReader/Tablet
:	PDF

< >This is the last of three volumes about 'Simple Lie Algebras over Fields of Positive Characteristic' by Helmut Strade, presenting the state of the art of the structure and classification of Lie algebras over fields of positive characteristic. In this monograph the proof of the Classification Theorem presented in the first volume is concluded. It colle ts all the important results on the topic which can be found only in scattered scientific literatur so far.

< >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