论文标题
$ \ frac {1} {2} $ - 谎言代数和转泊泊松代数的推导
$\frac{1}{2}$-derivations of Lie algebras and transposed Poisson algebras
论文作者
论文摘要
建立了$ \ frac {1} {2} $之间的关系 - lie代数的衍生物和转泊泊松代数。一些非平凡的转移泊松代数，具有一定的代数（witt代数，代数$ \ Mathcal {w}（a，-1）$，thin lie代数和可溶解的代数和Abelian nilpotent激进）。特别是，我们构建了一个与劳伦（Laurent）多项式和witt代数同构的转移泊松代数的例子。 On the other side, it was proven that there are no non-trivial transposed Poisson algebras with Lie algebra part isomorphic to a semisimple finite-dimensional algebra, a simple finite-dimensional superalgebra, the Virasoro algebra, $N=1$ and $N=2$ superconformal algebras, or a semisimple finite-dimensional $ n $ -lie代数。
A relation between $\frac{1}{2}$-derivations of Lie algebras and transposed Poisson algebras was established. Some non-trivial transposed Poisson algebras with a certain Lie algebra (Witt algebra, algebra $\mathcal{W}(a,-1)$, thin Lie algebra and solvable Lie algebra with abelian nilpotent radical) were constructed. In particular, we constructed an example of the transposed Poisson algebra with associative and Lie parts isomorphic to the Laurent polynomials and the Witt algebra. On the other side, it was proven that there are no non-trivial transposed Poisson algebras with Lie algebra part isomorphic to a semisimple finite-dimensional algebra, a simple finite-dimensional superalgebra, the Virasoro algebra, $N=1$ and $N=2$ superconformal algebras, or a semisimple finite-dimensional $n$-Lie algebra.
