Transposed Poisson structures

Transposed Poisson structures on Block Lie algebras and superalgebras

“…1 2 -derivations and transposed Poisson structures of solvable Lie algebras. It is known that each finite-dimensional nilpotent Lie algebra has a non-trivial transposed Poisson structure ( 1 2derivations, 1 2 -biderivations) [8,Theorem 14]. These results are motivating the question of the existence of non-trivial 1 2 -derivations of solvable Lie algebras, which will be answered in the present subsection.…”

“…More significantly, a transposed Poisson algebra naturally arises from a Novikov-Poisson algebra by taking the commutator Lie algebra of the Novikov algebra. Thanks to [4], any unital transposed Poisson algebra is a particular case of a "contact bracket" algebra and a quasi-Poisson algebra. Later, in a recent paper by Ferreira, Kaygorodov, and Lopatkin a relation between 1 2 -derivations of Lie algebras and transposed Poisson algebras has been established [7].…”

“…Later, in a recent paper by Ferreira, Kaygorodov, and Lopatkin a relation between 1 2 -derivations of Lie algebras and transposed Poisson algebras has been established [7]. These ideas were used to describe all transposed Poisson structures on Witt and Virasoro algebras in [7]; on twisted Heisenberg-Virasoro, Schrödinger-Virasoro and extended Schrödinger-Virasoro algebras in [19]; on oscillator algebras in [4]. It was proved that each complex finite-dimensional solvable Lie algebra has a non-trivial transposed Poisson structure [14].…”

“…The Homand BiHom-versions of transposed Poisson algebras and transposed Poisson bialgebras have been considered in [3,15,16]. For the list of actual open questions on transposed Poisson algebras see [4].…”

The algebraic and geometric classification of transposed Poisson algebras

“…More significantly, a transposed Poisson algebra naturally arises from a Novikov-Poisson algebra by taking the commutator Lie algebra of the Novikov algebra. Unital transposed Poisson algebras are studied in [5]. The Hom-and BiHom-versions of transposed Poisson algebras are considered in [29,30].…”