$\delta$-biderivations of Virasoro related algebras

TL;DR

This paper classifies all $delta$-biderivations for several important infinite-dimensional Lie algebras, including the Witt, Virasoro, and related $W$-algebras, providing foundational insights into their algebraic structures.

Contribution

It explicitly determines the $delta$-biderivations for key Virasoro related algebras and their central extensions, a novel comprehensive analysis in this area.

Findings

Complete classification of $delta$-biderivations for the Witt algebra

Explicit determination of $delta$-biderivations for the Virasoro algebra

Applications to the structure and representation theory of these algebras

Abstract

We determine all $\delta$-biderivations for the Witt algebra, the Virasoro algebra, the $W$-algebras $W(a,b)$ and their universal central extensions $\widetilde W(a,b)$, and then give some applications.