Local derivations and local automorphisms on the super Virasoro algebras

TL;DR

This paper proves that all local derivations and local or 2-local automorphisms on super-Virasoro algebras are actually derivations and automorphisms, respectively, clarifying their structural properties.

Contribution

It establishes that every local derivation is a derivation and every local or 2-local automorphism is an automorphism on super-Virasoro algebras, providing new insights into their algebraic structure.

Findings

Every local derivation is a derivation.

Every local automorphism is an automorphism.

Every 2-local automorphism is an automorphism.

Abstract

This paper aims to study the local derivations, 2-local automorphisms and local automorphisms on the super-Virasoro algebras. The primary focus is to establish that every local derivation of the super-Virasoro algebras is indeed a derivation, and to demonstrate that every local or 2-local automorphism of the super-Virasoro algebras is an automorphism.