Maximal Subalgebras for Lie Superalgebras of Cartan Type

TL;DR

This paper classifies maximal graded subalgebras of Lie superalgebras of Cartan type over fields of prime characteristic, providing complete descriptions and dimension formulas, and reduces the problem to classical Lie superalgebras.

Contribution

It offers a comprehensive classification of maximal graded subalgebras for Cartan type Lie superalgebras, linking the problem to classical cases.

Findings

Complete description of maximal reducible graded subalgebras.

Dimension formulas for these subalgebras.

Reduction of classification to classical Lie superalgebras.

Abstract

The maximal graded subalgebras for four families of Lie superalgebras of Cartan type over a field of prime characteristic are studied. All maximal reducible graded subalgebras are described completely and their isomorphism classes, dimension formulas are found. The classification of maximal irreducible graded subalgebras is reduced to the classification of the maximal irreducible subalgebras for the classical Lie superalgebras $\frak{gl}(m,n)$, $\frak{sl}(m,n)$ and $\frak{osp}(m,n)$.