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<p>In this paper, we describe transposed Poisson algebra structures on the Heisenberg–Virasoro algebra <i>L</i> of rank two and its generalization <i>L</i>(<i>p</i>, <i>q</i>), where <i>p</i>, <i>q</i> ∈ ℂ. We show that transposed Poisson algebra structures are trivial on <i>L</i> as well as on <i>L</i>(<i>p</i>, <i>q</i>) when (<i>p</i>, <i>q</i>) ∉ ℤ × ℤ. We then describe all nontrivial transposed Poisson algebra structures on <i>L</i>(<i>p</i>, <i>q</i>) for (<i>p</i>, <i>q</i>) ∈ ℤ × ℤ. Specifically, we classify the nontrivial transposed Poisson algebra structures on <i>L</i>(0, 0).</p>

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Transposed Poisson Algebra Structures on Generalized Heisenberg–Virasoro Algebra of Rank Two

  • 期刊论文

  • 发表日期：

    2025年7月15日

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  • Yi Wen,
  • Naihuan Jing,
  • Jiancai Sun,
  • Honglian Zhang

摘要

In this paper, we describe transposed Poisson algebra structures on the Heisenberg–Virasoro algebra L of rank two and its generalization L(p, q), where p, q ∈ ℂ. We show that transposed Poisson algebra structures are trivial on L as well as on L(p, q) when (p, q) ∉ ℤ × ℤ. We then describe all nontrivial transposed Poisson algebra structures on L(p, q) for (p, q) ∈ ℤ × ℤ. Specifically, we classify the nontrivial transposed Poisson algebra structures on L(0, 0).