On the simple transposed Poisson algebras and Jordan superalgebras
Rings and Algebras
2023-05-30 v2
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. Furthermore, we show that the Kantor double of a transposed Poisson algebra is a Jordan superalgebra. Additionally, a simplicity criterion for the Kantor double of a transposed Poisson algebra is obtained.
Keywords
Cite
@article{arxiv.2305.13848,
title = {On the simple transposed Poisson algebras and Jordan superalgebras},
author = {Amir Fernández Ouaridi},
journal= {arXiv preprint arXiv:2305.13848},
year = {2023}
}
Comments
10 pages, added references, added Theorem 30, minor typos corrected