# Local superderivations on Cartan type Lie superalgebras

## TL;DR

This paper characterizes local superderivations on Cartan type Lie superalgebras over complex numbers and proves they coincide with superderivations, also extending results to 2-local superderivations.

## Contribution

It provides a complete characterization of local and 2-local superderivations on Cartan type Lie superalgebras, showing they are all superderivations.

## Key findings

- Every local superderivation is a superderivation.
- Every 2-local superderivation is a superderivation.
- Results apply to Cartan type simple Lie superalgebras.

## Abstract

In this paper, we characterize the local superderivations on Cartan type Lie superalgebras over the complex field $\mathbb{C}$. Furthermore, we prove that every local superderivations on Cartan type simple Lie superalgebras is a superderivations. As an application, using the results on local superderivations we characterize the $2$-local superderivations on Cartan type Lie superalgebras. We prove that every $2$-local superderivations on Cartan type Lie superalgebras is a superderivations.