This analysis describes Poisson structures in non-finitely graded Lie algebras, indicating no non-trivial associative structures exist.
Let [Formula: see text] be a class of non-finitely graded Lie algebras related to generalized Witt algebras [Formula: see text]. We give a full description of the Poisson structures on [Formula: see text]. It is shown that there is no non-trivial and associative Poisson algebraic structures on [Formula: see text].
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Xu et al. (2026) studied this question.
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