Local superderivation and super-biderivation on generalized quaternion algebra

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.