Classifying the Absolute Toral Rank Two Case.

Intro -- Contents -- Introduction -- 10. Tori in Hamiltonian and Melikian algebras -- 10.1 Determining absolute toral ranks of Hamiltonian algebras -- 10.2 More on H(2 -- (1,2))(2)[ p] -- 10.3 2-dimensional tori in H(2 -- 1 -- Φ(τ ))(1) -- 10.4 Semisimple elements in H(2 -- 1 -- Φ(1))[ p] -- 10.5 Melikian algebras -- 10.6 Semisimple Lie algebras of absolute toral rank 1 and 2 -- 10.7 Weights -- 11. 1-sections -- 11.1 Lie algebras of absolute toral rank 1 -- 11.2 1-sections -- 11.3 Representations of dimension &lt -- p2 -- 11.4 More on H(2 -- 1)(2) -- 11.5 Low dimensional representations of H(2 -- 1)(2) -- 12. Sandwich elements and rigid tori -- 12.1 Deriving identities -- 12.2 Sandwich elements -- 12.3 Rigid roots -- 12.4 Rigid tori -- 12.5 Trigonalizability -- 13. Towards graded algebras -- 13.1 The pentagon -- 13.2 An upper bound -- 13.3 Filtrations -- 13.4 More on Hamiltonian roots -- 13.5 Switching tori -- 13.6 Good triples -- 13.7 On the existence of good tori and good triples -- 14. The toral rank 2 case -- 14.1 No root is exceptional -- 14.2 S is not of Cartan type -- 14.3 Graded counterexamples -- Notation -- Bibliography -- Index.

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