Support for Integrable Hopf Algebras via Noncommutative Hypersurfaces
Support for Integrable Hopf Algebras via Noncommutative Hypersurfaces
复制标题
通过非交换超曲面支持可积 Hopf 代数
DOI：
10.1093/imrn/rnab264
复制
发表时间：
2021
影响因子：
1
通讯作者：
Pevtsova, Julia
中科院分区：
文献类型：
--
作者：
Negron, Cris;Pevtsova, Julia
本文考虑有限维Hopf代数，它允许有限整体维数的Noether Hopf代数的光滑变形.这类Hopf代数的例子包括复数上的小量子群、有限特征的限制包络代数和高群的Drinfeld双。我们提供了一种方法来分析（上同调）支持的表示在这样的，通过奇异类别的超曲面相关的功能上相应的参数化空间。我们使用这种超曲面的方法来建立张量积性质的上同调支持，为以下的例子：功能的有限群计划，Drinfeld双一定高度1可解有限群计划，玻色量子完全相交，和小量子Borel型。
We consider finite-dimensional Hopf algebrasthat admit a smooth deformationby a Noetherian Hopf algebraof finite global dimension. Examples of such Hopf algebras include small quantum groups over the complex numbers, restricted enveloping algebras in finite characteristic, and Drinfeld doubles of heightgroup schemes. We provide a means of analyzing (cohomological) support for representations over such, via the singularity categories of the hypersurfacesassociated with functionson the corresponding parametrization space. We use this hypersurface approach to establish the tensor product property for cohomological support, for the following examples: functions on a finite group scheme, Drinfeld doubles of certain height 1 solvable finite group schemes, bosonized quantum complete intersections, and the small quantum Borel in type.