论文标题
WITT类型代数的转泊泊松结构
Transposed Poisson structures on Witt type algebras
论文作者
论文摘要
我们描述了$ \ frac {1} {2} $ - 衍生物，因此在witt type lie代数$ v（f）$上进行了转移的泊松代数结构，其中$ f：γ\ to \ mathbb c $是非琐事和$ f（0）= 0 $。更确切地说，如果$ | f（γ）| \ ge 4 $，则$ v（f）$上的所有转移泊松代数结构是组代数结构$（v（f），\ cdot）$ on $ v（f）$的突变。如果$ | f（γ）| = 3 $，则我们获得$ 3 $子空间的直接总和为$ v（f）$，对应于$γ$中的$γ_0$的cosets，乘以$ \ cdot $的乘法不同。情况$ | f（γ）| = 2 $更为复杂，但也涉及$ \ cdot $的某些突变。结果，发现非平凡$ {\ rm hom} $的新的谎言代数 - lie代数结构。
We describe $\frac{1}{2}$-derivations, and hence transposed Poisson algebra structures, on Witt type Lie algebras $V(f)$, where $f:Γ\to\mathbb C$ is non-trivial and $f(0)=0$. More precisely, if $|f(Γ)|\ge 4$, then all the transposed Poisson algebra structures on $V(f)$ are mutations of the group algebra structure $(V(f),\cdot)$ on $V(f)$. If $|f(Γ)|=3$, then we obtain the direct sum of $3$ subspaces of $V(f)$, corresponding to cosets of $Γ_0$ in $Γ$, with multiplications being different mutations of $\cdot$. The case $|f(Γ)|=2$ is more complicated, but also deals with certain mutations of $\cdot$. As a consequence, new Lie algebras that admit non-trivial ${\rm Hom}$-Lie algebra structures are found.
