Simple Lie algebras of small characteristic. I: Sandwich elements
This paper is intended to contribute to the eventual classification of all simple Lie algebras of characteristics 5 and 7 by obtaining results analogous to a step in the already completed classification of such algebras for characteristic \(p > 7\). The authors investigate simple Lie algebras of absolute toral rank 2, an investigation in which sandwich elements have an important part. (An element \(c\) of a Lie algebra \(L\) is a sandwich of \(L\) if \((\text{ad} c)^2=0\).) The authors prove that if \(L\) is simple of absolute toral rank 2 over an algebraically closed field of characteristic \(p\geq 5\) and \(T\) is a 2-dimensional torus in the semisimple \(p\)-envelope of \(L\), then \(L\) is either classical or isomorphic to \(H(2;\mathbf{1};\Phi(\tau))^{(1)}\) or there is a 2-dimensional torus \(T'\) conjugate to \(T\) such that \(C_L(T')\) acts triangulably on \(L\) and \(L\) has homogeneous sandwiches with respect to \(T'\).
simple Lie algebras of characteristics 5 and 7
scientific article; zbMATH DE number 1013993
scientific article