Transposed Poisson structures on Virasoro-type algebras (Q6655054)

Recently, C. Bai, R. Bai, L. Guo and Y. Wu have introduced a dual notion of the Poisson algebra, called a transposed Poisson algebra, by exchanging the role of the two multiplications in the Leibniz rule defining the Poisson algebra. Let us also recall that a transposed Poisson algebra naturally arises from a Novikov-Poisson algebra. Moreover, any transposed Poisson algebra is a commutative Gelfand-Dorfman algebra.\N\NIn this paper, the authors follow the description of transposed Poisson structures obtained on the Witt algebra and have the purpose to find non trivial transposed Poisson structures. They obtain a description of the transposed Poisson structures on the deformed generalized Heisenberg-Virasova algebra \(g(G,\lambda)\). They prove that \(g(G,\lambda)\) admits nontrivial transposed structures if and only if \(\lambda=-1\). Examples are discussed.