Maximal subalgebras of simple modular Lie algebras
Let \(L\) be a restricted simple Lie algebra of Cartan type over an algebraically closed field of characteristic \(p>3\). The aim of the paper under review is to classify the maximal graded subalgebras \(M=M_{-2}\oplus M_{-1}\oplus M_0\oplus M_\oplus\cdots \oplus M_r\) of \(L\) where \(L\) has the standard grading \(L=L_{-2}\oplus L_{-1}\oplus L_0\oplus L_1\oplus\cdots\oplus L_r\) (and \(L_{-2}=0\) unless \(L\) is a contact algebra). A classification of those maximal graded subalgebras \(M\) of \(L\) (with \(L_{-2}=0\)) that contain \(L_{-1}\oplus L_0\) has previously been established by \textit{A. I. Kostrikin} and \textit{I. R. Shafarevich} [Izv. Akad. Nauk SSSR, Ser. Mat. 33, 251--322 (1969; Zbl 0211.05304)]. In the paper under review the author considers the remaining cases. He obtains an explicit construction unless \(M=L_{-2}\oplus L_{-1}\oplus M_0\oplus M_1\oplus\cdots\oplus M_r\) and \(M_0\) is a maximal subalgebra of \(L_0\) that acts irreducibly on \(L_{-1}\). In this case the problem is reduced to the classification of the irreducible maximal subalgebras of the simple classical Lie algebras which still is not complete.
restricted simple Lie algebra of Cartan type
scientific article; zbMATH DE number 2153328
scientific article