TY  - JOUR
T1  - Transposed Hom-Poisson and Hom-pre-Lie Poisson algebras
AU  - Silvestrov, Sergei
AU  - Laraiedh, Ismail
PY  - 2025
DA  - October
Y2  - 2025
DO  - 10.15672/hujms.1417353
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 1
EP  - 29
LA  - en
AB  - The purpose of this paper is introduce and give some constructions results and examples of transposed Hom-Poisson and Hom-pre-Lie Poisson algebras. Also, we establish the bimodules and matched pairs of transposed Hom-Poisson algebras. Their related relevant properties are also given. Finally, the notion of $\mathcal{O}$-operator is exploited to establish the relations between transposed Hom-Poisson and Hom-pre-Lie Poisson algebras.
KW  - transposed Hom-Poisson algebra
KW  - Hom-pre-LiePoisson algebra
KW  - bimodule
KW  - $\mathcal{O}$-operator
CR  - [1] E. Abdaoui, S. Mabrouk and A. Makhlouf, Rota-Baxter Operators on Pre-Lie Superalgebras, Bull. Malays. Math. Sci. Soc. 42, 1567-1606, 2019.
UR  - https://doi.org/10.15672/hujms.1417353
L1  - https://dergipark.org.tr/en/download/article-file/3650501
ER  -