The present paper is devoted to study 2-local superderivations on the super Virasoro algebra and the super W(2, 2) algebra. We prove that all 2local superderivations on the super Virasoro algebra as well as the super W(2, 2) algebra are (global) superderivations.

In this paper, all symmetric super-biderivations of some Lie superalgebras are determined. As an application, commutative post-Lie superalgebra structures on these Lie superalgebras are also obtained.

This paper is devoted to defining and studying Whittaker modules and high order Whittaker modules for the [Formula: see text] super-BMS3 algebra. We also classify the simple Whittaker modules and obtain the necessary and sufficient conditions for the irreducibility of these modules.

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With the Ω-operators for the Virasoro algebra [5] and the super Virasoro algebra in [10,9], we get the Ω-operators for the Ovsienko-Roger superalgebras in this paper and then use it to classify all simple cuspidal modules for the Z-graded and 1 2 Z-graded Ovsienko-Roger superalgebras. By this result, we can easily classify all simple Harish-Chandra modules over some related Lie superalgebras, including the N = 1 BMS 3 algebra, the super W (2, 2), etc.