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February 28, 2026Algebra Colloquium0 citations

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

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RXRunguo XuYXYing Xu

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.

Abstract

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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Cite This Study

Xu et al. (2026) studied this question.

synapsesocial.com/papers/69a288060a974eb0d3c03f54https://doi.org/10.1142/s1005386726000143
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