RT journal article
T1 On the simple transposed Poisson algebras and Jordan superalgebras
A1 Fernández Ouaridi, Amir
A2 Matemáticas
K1 Jordan superalgebra
K1 Lie algebra
K1 Poisson algebra
K1 Transposed Poisson algebra
AB 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.
PB Academic Press Inc.
SN 1090-266X
YR 2024
FD 2024
LK http://hdl.handle.net/10498/32643
UL http://hdl.handle.net/10498/32643
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026