@misc{10498/32643,
year = {2024},
url = {http://hdl.handle.net/10498/32643},
abstract = {We prove that a transposed Poisson algebra is simple if and only if its associated Lie bracket is simple. Consequently, any simple finite-dimensional transposed Poisson algebra over an algebraically closed field of characteristic zero is trivial. Similar results are obtained for transposed Poisson superalgebras. An example of a non-trivial simple finite-dimensional transposed Poisson algebra is constructed by studying the transposed Poisson structures on the modular Witt algebra. Furthermore, we show that the Kantor double of a transposed Poisson algebra is a Jordan superalgebra, that is, we prove that transposed Poisson algebras are Jordan brackets. Additionally, a simplicity criterion for the Kantor double of a transposed Poisson algebra is obtained.},
publisher = {Academic Press Inc.},
keywords = {Jordan superalgebra},
keywords = {Lie algebra},
keywords = {Poisson algebra},
keywords = {Transposed Poisson algebra},
title = {On the simple transposed Poisson algebras and Jordan superalgebras},
doi = {10.1016/J.JALGEBRA.2023.11.026},
author = {Fernández Ouaridi, Amir},
}