Transposed Poisson Structures on Generalized Block Lie Algebras and Superalgebras

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].