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.