Abstract

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].

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