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The mirror Heisenberg–Virasoro algebra Formula: see text is the semi-direct product of the Virasoro algebra and the twisted Heisenberg algebra. In this paper, all biderivations of the mirror Heisenberg–Virasoro algebra are determined by using the gradation of biderivations. As an application, we show that any linear commuting map Formula: see text on the mirror Heisenberg–Virasoro algebra is the form Formula: see text, where Formula: see text is an element from the basic field and Formula: see text is a linear map having its range in the center of Formula: see text.
Liu et al. (Wed,) studied this question.