使用$\textbf{U}_q$ -倾斜模块的蜂窝结构
Cellular structures using $\textbf{U}_q$-tilting modules
摘要：
利用$\textbf{U}_q$ -倾斜模理论构造中心化子代数的胞腔基。我们的方法是相当普遍的，适用于任何量子群$\textbf{U}_q$附加到一个Cartan矩阵，包括非半单的情况下，$q$是一个单位根和基域的正特征。我们的方法也推广到某些类别包含无限维模块。作为应用，我们给出了中心化子代数的一个新的半单性准则，并恢复了几个已知代数（具有部分新的胞腔基）的胞腔性，这些代数都符合我们的一般设置。
英文摘要：
We use the theory of $\textbf{U}_q$-tilting modules to construct cellular bases for centralizer algebras. Our methods are quite general and work for any quantum group $\textbf{U}_q$ attached to a Cartan matrix and include the non-semisimple cases for $q$ being a root of unity and ground fields of positive characteristic. Our approach also generalizes to certain categories containing infinite-dimensional modules. As applications, we give a new semisimplicty criterion for centralizer algebras, and recover the cellularity of several known algebras (with partially new cellular bases) which all fit into our general setup.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
