Maximal Subalgebras for Modular Graded Lie Superalgebras of Odd Cartan Type

TL;DR

This paper classifies all maximal graded subalgebras of certain finite-dimensional graded Lie superalgebras of odd Cartan type over fields with characteristic greater than 3, including reducible and irreducible cases.

Contribution

It provides a complete classification of maximal graded subalgebras for four series of odd Cartan type Lie superalgebras, reducing the irreducible case to classical Lie superalgebra analysis.

Findings

Classified all maximal graded subalgebras into three types.

Reduced the irreducible case to classical Lie superalgebra $rak{p}(n)$.

Established a comprehensive framework for understanding subalgebra structures.

Abstract

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 (\MyRoman{1}), (\MyRoman{2}) and (\MyRoman{3}). Maximal graded subalgebras of type (\MyRoman{3}) fall into reducible maximal graded subalgebras and irreducible maximal graded subalgebras. In this paper we classify maximal graded subalgebras of types (\MyRoman{1}), (\MyRoman{2}) and reducible maximal g raded subalgebras.The classification of irreducible maximal graded subalgebras is reduced to that of the irreducible maximal subalgebras of the classical Lie superalgebra $\mathfrak{p}(n)$.