# Super-biderivations of the contact Lie superalgebra $K(m,n;\underline{t})$

## TL;DR

This paper investigates the structure of super-biderivations in the contact Lie superalgebra $K(m,n; ext{ extunderscore}t)$ over a field with characteristic greater than 3, showing they are all inner using weight space decomposition.

## Contribution

It demonstrates that all skew-symmetric super-biderivations of $K(m,n; ext{ extunderscore}t)$ are inner, providing a detailed analysis based on the algebra's weight space decomposition.

## Key findings

- All super-biderivations are inner.
- Utilizes weight space decomposition for analysis.
- Provides structure results for contact Lie superalgebras.

## Abstract

Let $K$ denote the contact Lie superalgebra $K(m,n;\underline{t})$ over a field of characteristic $p>3$, which has a finite $\mathbb{Z}$-graded structure. Let $T_K$ be the canonical torus of $K$, which is an abelian subalgebra of $K_{0}$ and operates on $K_{-1}$ by semisimple endomorphisms. Utilizing the weight space decomposition of $K$ with respect to $T_K$, %we show the action of the skew-symmetric super-biderivation on the elements of $T$ and the contact of $K$. %Moreover, we prove that each skew-symmetric super-biderivation of $K$ is inner.