Mathematical analysis uncovers conditions for nontrivial transposed Poisson structures on generalized Block Lie algebras, revealing structural constraints across complex parameter spaces.
In this paper, transposed Poisson algebra structures on generalized Block Lie algebras [Formula: see text] and generalized Block Lie superalgebras [Formula: see text] are studied for arbitrary complex numbers [Formula: see text], [Formula: see text]. We determine [Formula: see text]-derivations of [Formula: see text] and [Formula: see text]-superderivations of [Formula: see text] to characterize their transposed Poisson structures. Specifically, transposed Poisson algebra structures on [Formula: see text] are nontrivial for [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text], while [Formula: see text] admits only trivial transposed Poisson superalgebra structures for [Formula: see text], [Formula: see text].
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Gu et al. (2026) studied this question.
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