Transposed Poisson structures on solvable and perfect Lie algebras
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910387477151744 |
|---|---|
| author | Kaygorodov, Ivan Khudoyberdiyev, Abror |
| author_facet | Kaygorodov, Ivan Khudoyberdiyev, Abror |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_00624 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Transposed Poisson structures on solvable and perfect Lie algebras Kaygorodov, Ivan Khudoyberdiyev, Abror Rings and Algebras 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. |
| title | Transposed Poisson structures on solvable and perfect Lie algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2310.00624 |