Skew-symmetric super-biderivations of the special Lie superalgebra S(m, n; t)

TL;DR

This paper investigates the structure of skew-symmetric super-biderivations in the special Lie superalgebra S(m, n; t), demonstrating that all such derivations are inner, using weight space decomposition and abelian subalgebras.

Contribution

It proves that all skew-symmetric super-biderivations of S(m, n; t) are inner, providing a detailed analysis using weight space decomposition.

Findings

All skew-symmetric super-biderivations are inner.

Utilized weight space decomposition to analyze derivations.

Characterized the action of derivations on specific subalgebras.

Abstract

This paper aims to study the skew-symmetric super-biderivations of the special Lie superalgebra S(m, n; t). Let S denote the special Lie superalgebra S(m, n; t) over a field of characteristic p > 2.Utilizing the abelian subalgebra TS and the weight space decomposition of S with respect to TS ,we show the action of a skew-symmetric super-biderivation on the elements of TS and some specific elements of S. Moreover, we prove that all skew-symmetric super-biderivations of S are inner.