Abstract
In the present paper, we introduce the notion of a δ-biderivation. First, we provide some properties of δ-biderivations and illustrate their applications. In particular, we establish a close relationship between -biderivations and transposed Poisson algebras. Second, we compute -derivations on the twisted Heisenberg–Virasoro, Schrödinger–Virasoro, extended Schrödinger–Virasoro and twisted Schrödinger–Virasoro algebras, respectively. It turns out that they have no nontrivial -derivations. Hence they have neither nonzero -biderivations nor nontrivial transposed Poisson algebra structures. Third, we classify transposed Poisson algebra structures on the Heisenberg and some current Lie algebras. This enables us to provide examples of Lie algebras having nontrivial transposed Poisson algebra structures.
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