Skew-symmetric super-biderivations of the Hamiltonian superalgebra H(m, n; t)

TL;DR

This paper investigates the structure of skew-symmetric super-biderivations in the Hamiltonian superalgebra H(m, n; t), demonstrating that all such derivations are inner, using weight space decomposition and subalgebra analysis.

Contribution

It establishes that all skew-symmetric super-biderivations of H(m, n; t) are inner, providing a complete characterization of these derivations in the context of Hamiltonian superalgebras.

Findings

All skew-symmetric super-biderivations are inner.

Utilized weight space decomposition to analyze derivations.

Characterized derivations using abelian subalgebra TH.

Abstract

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