Rootsystems of simple Lie algebras
This paper continues the investigation of the preceding article (cf. Zbl 0578.17010). -- It is shown that if \(L=\sum_{a\in R}L_ a\) is a simple nonclassical symmetric Lie algebra whose root system \(R\) contains no 2-section of type \(T_ 2\), then \(R\) is an irreducible Witt root system (i.e. with all nonzero roots Witt). Irreducible Witt root systems of prime rank (i.e. over \(\mathbb Z_ p)\) three are classified. Finally it is shown that the irreducible components of a Witt root system \(R\) are groups if and only if \(R\) excludes two specific types of irreducible Witt root systems of prime rank three. See also the following review Zbl 0578.17012.
scientific article; zbMATH DE number 3925051