论文标题
在加利利和可解决的谎言代数上转移的泊松结构
Transposed Poisson structures on Galilean and solvable Lie algebras
论文作者
论文摘要
描述了复杂的伽利亚型谎言和超级半骨的转移泊松结构。事实证明，所有主要的Galilean Lie代数都不具有非平凡的$ \ frac {1} {2} $ - 衍生物，并且随着它们的遵循，他们不承认非平凡的转移泊松结构。另外，我们证明了每个复杂的有限差解决方案代数都承认了一个非平凡的转移泊松结构和非平凡的$ {\ rm hom} $ - 谎言结构。
Transposed Poisson structures on complex Galilean type Lie algebras and superalgebras are described. It was proven that all principal Galilean Lie algebras do not have non-trivial $\frac{1}{2}$-derivations and as it follows they do not admit non-trivial transposed Poisson structures. Also, we proved that each complex finite-dimensional solvable Lie algebra admits a non-trivial transposed Poisson structure and a non-trivial ${\rm Hom}$-Lie structure.
