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The new concept of an absolute toral rank for subalgebras in arbitrary modular Lie algebras is introduced. All nonsimple Lie algebras of absolute toral rank ≤2 are determined in terms of smaller constituents. The final result is the first step towards the classification of all simple modular Lie algebras.
It is shown that all the irreducible integrable highest-weight modules for a Kac-Moody algebra of type Cℓ(1), and a large class of those for type Dℓ(1), can be constructed by essentially the same formalism as that employed for certain fundamental modules by Frenkel, Kac-Peterson and Feingold-Frenkel. The idea is to replace the Clifford algebra (or Weyl algebra) by higher analogues...
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