Classification of simple transposed Poisson n-Lie algebras

Determine explicit examples and a complete classification of simple transposed Poisson n-Lie algebras for arbitrary order n, including a precise description of all isomorphism classes and structural properties that distinguish them.

Background

The paper focuses on classifying 3-dimensional transposed Poisson 3-Lie algebras under specific conditions and references broader classification efforts for n-Lie algebras and transposed Poisson structures. In this context, the authors cite a question from Beites, Ferreira, and Kaygorodov regarding the classification of simple transposed Poisson n-Lie algebras, highlighting a gap in the literature on higher-order structures.