论文标题
泊松代数的退化
Degenerations of Poisson algebras
论文作者
论文摘要
我们构建了一种获取在交换代数定义的泊松代数的代数分类的方法，并将其应用于获得$ 3 $维泊松代数的分类。此外，我们研究了几何分类，变性图和轨道的封闭，各种$ 3 $维泊松代数。最后，我们还研究了在交换性无效的或丝状代数定义的泊松代数的代数分类，并且为了丰富该分类，我们研究了这些特定的泊松代数之间的脱落。
We construct a method to obtain the algebraic classification of Poisson algebras defined on a commutative associative algebra, and we apply it to obtain the classification of the $3$-dimensional Poisson algebras. In addition, we study the geometric classification, the graph of degenerations and the closures of the orbits of the variety of $3$-dimensional Poisson algebras. Finally, we also study the algebraic classification of the Poisson algebras defined on a commutative associative null-filiform or filiform algebra and, to enrich this classification, we study the degenerations between these particular Poisson algebras.
