论文标题
在有限的W-Superalgebras的前提下
On the Premet conjecture for finite W-superalgebras
论文作者
论文摘要
让$ \ bullet^†$是Losev的地图，它将有限的W-代数的两个方面理想发送给相应的Lie代数的通用包围代数。在\ cite {lo11}中证明的前提猜想说，仅限于具有有限的编imension的原始理想集，地图$ \ bullet^†$的任何光纤都是有限组的单个轨道。在本文中，我们在超级案例中制定并证明了类似的事实。这将为W-Superalgebras的一组有限维数表示，提供$ c_ {e} $是一个琐碎的群体，并且已知相应的通用封闭代数的原始理想集。
Let $\bullet^†$ be the map in sense of the Losev, which sends the set of two sided ideals of a finite W-algebras to that of the universal enveloping algebra of corresponding Lie algebras. The Premet conjecture which was proved in \cite{Lo11}, says that, restricted to the set of primitive ideals with finite codimension, any fiber of the map $\bullet^†$ is a single orbit under an action of a finite group. In this article we formulate and prove a similar fact in the super case. This will give a classification to the set of finite dimensional irreducible representations of W-superalgebras provided $C_{e}$ is a trivial group and the set of primitive ideals of the corresponding universal enveloping algebra of Lie superalgebra is known.
