MAXIMAL SUBALGEBRAS FOR MODULAR GRADED LIE SUPERALGEBRAS OF ODD CARTAN TYPE

The purpose of this paper is to determine all maximal graded subalgebras of the four infinite series of finite-dimensional graded Lie superalgebras of odd Cartan type over an algebraically closed field of characteristic p > 3. All maximal graded subalgebras consist of three types (I), (II) and (III). Maximal graded subalgebras of type (III) fall into reducible maximal graded subalgebras and irreducible maximal graded subalgebras. In this paper we classify maximal graded subalgebras of types (I), (II) and reducible maximal graded subalgebras. The classification of irreducible maximal graded subalgebras is reduced to that of the irreducible maximal subalgebras of the classical Lie superalgebra p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathfrak{p} $$\end{document}(n).