Estruturas de transposed poisson sobre álgebras e superálgebras de Lie

Abstract

This dissertation aims to study transposed Poisson algebras, highlighting their similarities with Poisson algebras and exploring their connections with other algebraic structures. We also examine transposed Poisson superalgebras and their properties. Furthermore, we establish a relationship between 1 2-derivations of Lie algebras and transposed Poisson algebras, showing that all transposed Poisson algebra structures with a certain Lie com ponent can be fully described. This connection is then used to characterize transposed Poisson structures over Witt-type algebras and Virasoro-type algebras. Finally, we present a classification of 3-dimensional transposed Poisson algebras based on the analysis of 1 2-derivations of 3-dimensional Lie algebras