论文标题
高图代数的Weyl模块和Weyl函子
Weyl modules and Weyl functors for hyper-map algebras
论文作者
论文摘要
我们研究了与地图代数$ \ mathfrak g \ otimes \ mathcal a $相关的超胺的表示，其中$ \ mathfrak g $是任何有限二维复杂的简单复杂的简单的lie代数和$ \ mathcal a $是任何关联的通勤词汇，均与乘以倍增的基础。我们考虑局部和全局WEYL模块的自然定义，以及这些代数的Weyl函子。在某些条件下，我们证明这些模块满足了某些通用性能，并且我们还为局部或全局WEYL模块提供了有限维度或有限生成的条件。
We investigate the representations of the hyperalgebras associated to the map algebras $\mathfrak g\otimes \mathcal A$, where $\mathfrak g$ is any finite-dimensional complex simple Lie algebra and $\mathcal A$ is any associative commutative unitary algebra with a multiplicatively closed basis. We consider the natural definition of the local and global Weyl modules, and the Weyl functor for these algebras. Under certain conditions, we prove that these modules satisfy certain universal properties, and we also give conditions for the local or global Weyl modules to be finite-dimensional or finitely generated, respectively.
