Local superderivation and super-biderivation on generalized quaternion algebra

TL;DR

This paper studies superderivations and super-biderivations on generalized quaternion algebras viewed as Lie superalgebras, proving that all local superderivations are actual superderivations.

Contribution

It establishes that on generalized quaternion algebras, every local superderivation coincides with a superderivation, extending understanding of derivation structures in Lie superalgebras.

Findings

All local superderivations are superderivations on generalized quaternion algebras.

Provides structural insights into Lie superalgebra derivations.

Enhances the theory of superderivations in algebraic structures.

Abstract

Let $\mathcal{H}^{a,b}$ be the generalized quaternion algebra over a unitary commutative ring. This paper aims to investigate super-biderivations and local superderivations on the generalized quaternion algebra, which is viewed as a class of Lie superalgebra. It turns out that on generalized quaternion algebras, any local superderivation is a superderivation.