# New simple modular Lie superalgebras as generalized prolongs

## TL;DR

This paper explores the prolongations of simple finite-dimensional Lie superalgebras over fields with characteristic p>2, discovering new simple superalgebras and classifying those with rank 2 Cartan matrices.

## Contribution

It introduces new simple Lie superalgebras, including superBrown and superMelikyan, and classifies rank 2 Cartan matrix superalgebras, expanding the understanding of modular Lie superalgebras.

## Key findings

- Discovered several new simple Lie superalgebras, including superBrown and superMelikyan.
- Classified simple Lie superalgebras with Cartan matrix of rank 2.
- Analyzed prolongations of simple Lie superalgebras over fields with characteristic p>2.

## Abstract

Over algebraically closed fields of characteristic p>2, prolongations of the simple finite dimensional Lie algebras and Lie superalgebras with Cartan matrix are studied for certain simplest gradings of these algebras. Several new simple Lie superalgebras are discovered, serial and exceptional, including superBrown and superMelikyan superalgebras. Simple Lie superalgebras with Cartan matrix of rank 2 are classified.