Transposed Poisson structures on solvable and perfect Lie algebras

Abstract

We described all transposed Poisson algebra structures on oscillator Lie algebras, i.e., on one-dimensional solvable extensions of the $(2n+1)$-dimensional Heisenberg algebra; on solvable Lie algebras with naturally graded filiform nilpotent radical; on $(n+1)$-dimensional solvable extensions of the $(2n+1)$-dimensional Heisenberg algebra; and on $n$-dimensional solvable extensions of the $n$-dimensional algebra with the trivial multiplication. We also gave an answer to one question on transposed Poisson algebras early posted in a paper by Beites, Ferreira, and Kaygorodov. Namely, we found a finite-dimensional Lie algebra with non-trivial $\frac{1}{2}$-derivations, but without non-trivial transposed Poisson algebra structures.

arXiv commentarXiv admin note: text overlap with arXiv:2207.00281, arXiv:2305.00727

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Cited by in corpus (1)

• Transposed Poisson structures