论文标题
通过非交通性超曲面支持可集成的HOPF代数
Support for integrable Hopf algebras via noncommutative hypersurfaces
论文作者
论文摘要
我们考虑有限的HOPF代数$ U $，该$ u $ u $ u \ u $ u \ u $ to u $ to u $ to u $ to u $ to u $ a noeTherian hopf代数$ u $的有限全球尺寸。此类HOPF代数的示例包括在复数上的小量子组，限制有限特征的代数包围，以及Drinfeld的高度$ 1 $ 1 $组方案。我们通过相应的参数化空间上与功能$ f $相关的HyperSurfaces $ u/（f）$的奇异性类别提供了对此类$ U $表示表示的表示（共同体）支持的方法。我们使用这种超表面方法来建立张量产品的共同体支持，以下示例：在有限组方案中的功能，一定高度的Drinfeld双打1个可溶解的有限组方案，实用的量子量子共同交叉点，以及类型$ a $的小量子Borel。
We consider finite-dimensional Hopf algebras $u$ which admit a smooth deformation $U\to u$ by a Noetherian Hopf algebra $U$ of 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 height $1$ group schemes. We provide a means of analyzing (cohomological) support for representations over such $u$, via the singularity categories of the hypersurfaces $U/(f)$ associated to functions $f$ on 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 $A$.
