论文标题
在块上的底座结构和超级骨架上的转移泊松结构
Transposed Poisson structures on Block Lie algebras and superalgebras
论文作者
论文摘要
我们描述了块上的转泊泊松代数结构$ \ MATHCAL B（Q）$和Block Lie Superalgebras $ \ Mathcal S（Q）$，其中$ Q $是任意的复杂数字。具体来说，我们表明，只要$ q \ not \ in \ mathbb z $，$ \ mathcal b（q）$上的转泊泊松结构都是微不足道的，而对于\ mathbb z $中的每一个$ q \ in \ mathbb z $都只有一个（iSomorphismismist osmorphismist）在$ \ mathcal b（q）上只有一个（iensomorphismismist）。 Superalgebra $ \ Mathcal S（Q）$仅接受$ q \ ne 0 $的琐碎的托盘泊松式超级级结构和两个非同构的非晶状型poisson superalgebra结构，$ q = 0 $。结果，发现了非平凡的$ {\ rm hom} $ - lie代数结构的新的谎言代数和超级法。
We describe transposed Poisson algebra structures on Block Lie algebras $\mathcal B(q)$ and Block Lie superalgebras $\mathcal S(q)$, where $q$ is an arbitrary complex number. Specifically, we show that the transposed Poisson structures on $\mathcal B(q)$ are trivial whenever $q\not\in\mathbb Z$, and for each $q\in\mathbb Z$ there is only one (up to an isomorphism) non-trivial transposed Poisson structure on $\mathcal B(q)$. The superalgebra $\mathcal S(q)$ admits only trivial transposed Poisson superalgebra structures for $q\ne 0$ and two non-isomorphic non-trivial transposed Poisson superalgebra structures for $q=0$. As a consequence, new Lie algebras and superalgebras that admit non-trivial ${\rm Hom}$-Lie algebra structures are found.
