Transposed Poisson structures on Block Lie algebras and superalgebras

We describe transposed Poisson algebra structures on Block Lie algebras B(q) and superalgebras S(q), where q is an arbitrary complex number. Specifically, we show that the are trivial whenever q∉Z, for each q∈Z there only one (up to isomorphism) non-trivial structure B(q). The superalgebra S(q) admits q≠0 two non-isomorphic q=0. As a consequence, new admit Hom-Lie found.