Skew-symmetric super-biderivations of the special odd Hamiltonian superalgebra SHO(n, n; t)

TL;DR

This paper investigates the structure of skew-symmetric super-biderivations in the special odd Hamiltonian superalgebra SHO(n, n; t), revealing that all such derivations are inner, using weight space decomposition techniques.

Contribution

It demonstrates that all skew-symmetric super-biderivations of SHO(n, n; t) are inner, providing a complete characterization of these derivations.

Findings

All skew-symmetric super-biderivations of SHO are inner.

Utilized weight space decomposition to analyze derivations.

Identified the action of derivations on specific elements of SHO.

Abstract

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