Toral rank one simple Lie algebras of low characteristics
The author classifies the toral rank one simple Lie algebras over algebraically closed fields of characteristic \(p=2,3\). This corresponds to one of the basic steps in the successful classification of the simple finite-dimensional Lie algebras over algebraically closed fields of characteristic \(p>7\). His result is that \(sl(2)\) and \(psl(3)\) are the only such algebras for \(p=3\), and no such algebras exist for \(p=2\). The techniques required for this classification in small characteristics differ significantly from those that have been used in the case \(p>7\). In the process of this study the author has also obtained results on such topics as simple Lie algebras \(L\) containing a Cartan subalgebra of toral rank 1 in \(L\) and the structure of certain exceptional Hamiltonian algebras of characteristic 3.
exceptional Hamiltonian algebras of characteristic 3
scientific article; zbMATH DE number 1139794
scientific article