# Conformal biderivations of loop $W(a,b)$ Lie conformal algebra

## TL;DR

This paper investigates conformal biderivations within specific Lie conformal algebras, providing classifications and revealing that all biderivations on the Virasoro algebra are inner, advancing understanding of their algebraic structure.

## Contribution

It classifies conformal biderivations for loop W(a,b), loop Virasoro, and Virasoro Lie conformal algebras, showing all on Virasoro are inner, which is a novel result.

## Key findings

- All conformal biderivations on Virasoro Lie conformal algebra are inner.
- Explicit descriptions of conformal biderivations for loop W(a,b) and loop Virasoro algebras.
- Classification results contribute to the structural theory of Lie conformal algebras.

## Abstract

In this paper, we study conformal biderivations of a Lie conformal algebra. First, we give the definition of conformal biderivation. Next, we determine the conformal biderivations of loop $W(a,b)$ Lie conformal algebra, loop Virasoro Lie conformal algebra and Virasoro Lie conformal algebra. Especially, all conformal biderivations on Virasoro Lie conformal algebra are inner conformal biderivations.