Poisson Structures of Non-finitely Graded Lie Algebras Related to Generalized Witt Algebras

Key Points

• The aim is to explore and describe the Poisson structures associated with a class of non-finitely graded Lie algebras linked to generalized Witt algebras.
• Examined the Poisson structures on the designated class of Lie algebras.
• Analyzed the associative properties within these algebraic structures.
• Demonstrated the lack of non-trivial associative Poisson algebraic structures on the considered Lie algebras.