论文标题
本地环上的量子倾斜模块
Quantum tilting modules over local rings
论文作者
论文摘要
我们表明，存在量子组的量子组的倾斜模块存在，并且不可分解的倾斜模块由其最高权重参数化。为此，我们介绍了一个模型类别$ {\ MATHCAL X} = {\ MATHCAL X} _ {\ MATHSCR A}（r）$与Noetherian $ {\ Mathbb z}相关的$我们表明，如果$ {\ mathscr a} $是量子特征$ 0 $，则模型类别包含所有$ u _ {\ mathscr a} $ - 容纳Weyl过滤的模块。如果$ {\ mathscr a} $是本地的，则我们研究模型类别中的扭转现象。这导致在$ {\ Mathcal X} $中构建无扭转的对象。我们表明，这些对应于与$ {\ mathscr a} $和$ r $相关的量子组的倾斜模块。
We show that tilting modules for quantum groups over local Noetherian domains exist and that the indecomposable tilting modules are parametrized by their highest weight. For this we introduce a model category ${\mathcal X}={\mathcal X}_{\mathscr A}(R)$ associated with a Noetherian ${\mathbb Z}[v,v^{-1}]$-domain ${\mathscr A}$ and a root system $R$. We show that if ${\mathscr A}$ is of quantum characteristic $0$, the model category contains all $U_{\mathscr A}$-modules that admit a Weyl filtration. If ${\mathscr A}$ is in addition local, we study torsion phenomena in the model category. This leads to a construction of torsion free objects in ${\mathcal X}$. We show that these correspond to tilting modules for the quantum group associated with ${\mathscr A}$ and $R$.
