# Restricted Central Extensions of Restricted Heisenberg Lie Superalgebras

## TL;DR

This paper investigates the structure of restricted Heisenberg Lie superalgebras over fields of characteristic p > 2, focusing on their cohomology and central extensions, providing explicit descriptions of these extensions.

## Contribution

It computes the restricted 2-cohomology spaces and describes the associated one-dimensional central extensions for restricted Heisenberg Lie superalgebras.

## Key findings

- Computed restricted 2-cohomology spaces.
- Described the structure of restricted one-dimensional central extensions.
- Provided explicit classifications of these extensions.

## Abstract

Restricted Heisenberg Lie superalgebras are studied over an algebraically closed field F of characteristic p > 2. We use the ordinary 1- and 2-cohomology spaces with trivial coefficients to compute the restricted 2-cohomology spaces. As an application, the corresponding restricted one-dimensional central extensions are described.