论文标题
确切的因素化和有限张量类别的扩展
Exact factorizations and extensions of finite tensor categories
论文作者
论文摘要
我们将\ cite {g}扩展到非膜壳案例。我们将有限张量类别的类别$ \ b = \ a \ b = b = b = \ b = c $定义和研究确切的因素化$ \ b $ $ \ b $成两个张量子子类别的产品$ \ a，\ c \ subset \ b $，并将有限技术类别的确切序列类别与精确的tensor类别相关。我们应用结果来研究准HOPF代数的确切因素，并通过另一个研究有限组方案的理论张量类别\ cite {g2}的扩展。我们还提供了几个示例来说明我们的结果。
We extend \cite{G} to the nonsemisimple case. We define and study exact factorizations $\B=\A\bullet \C$ of a finite tensor category $\B$ into a product of two tensor subcategories $\A,\C\subset \B$, and relate exact factorizations of finite tensor categories to exact sequences of finite tensor categories with respect to exact module categories \cite{EG}. We apply our results to study exact factorizations of quasi-Hopf algebras, and extensions of a finite group scheme theoretical tensor category \cite{G2} by another one. We also provide several examples to illustrate our results.
