Biderivations of W-algebra $W(2,2)$ and Virasoro algebra without skewsymmetric condition and their applications

TL;DR

This paper characterizes biderivations of the W-algebra $W(2,2)$ and Virasoro algebra without the skewsymmetric condition, identifying non-inner biderivations and applications to linear commuting maps.

Contribution

It introduces a new characterization of biderivations without skewsymmetric constraints and identifies non-inner biderivations for these algebras.

Findings

Identified two classes of non-inner biderivations.

Derived forms of linear commuting maps on $W(2,2)$ and $Vir$.

Extended understanding of algebraic structures without skewsymmetric assumptions.

Abstract

In this paper, we characterize the biderivations of W-algebra $W(2,2)$ and Virasoro algebra $Vir$ without skewsymmetric condition. We get two classes of non-inner biderivations. As applications, we also get the forms of linear commuting maps on W-algebra $W(2,2)$ and Virasoro algebra $Vir$.