论文标题
某些量子组在路径代数上的HOPF动作
Hopf actions of some quantum groups on path algebras
论文作者
论文摘要
我们的第一个量子borel $ u_q（\ mathfrak {b}）\ subset u_q（\ mathfrak {sl} _2）$的量子borel $ u_q（\ mathfrak {b}）$的第一个集合的结果集合（过滤）。当$ q $是团结的根源时，我们为这些动作提供了必要的条件，可以通过相应的有限维使用者，广义taft代数$ t（r，n）$和小量子组$ u_q（\ mathfrak {sl {sl} _2 _2）$进行分解。 在本文的第二部分中，我们转向张量类别的语言。在这里，我们认为配备了HOPF代数$ h $的动作的Quiver Path Algebra，以作为张量表示的张量代数$ h $。这种张量代数是由该张量类别中的代数和bimodule生成的。我们的第二个结果集合通过与某些明确描述的与关系的表达类别相等地描述了相应的双模型类别。
Our first collection of results parametrize (filtered) actions of a quantum Borel $U_q(\mathfrak{b}) \subset U_q(\mathfrak{sl}_2)$ on the path algebra of an arbitrary (finite) quiver. When $q$ is a root of unity, we give necessary and sufficient conditions for these actions to factor through corresponding finite-dimensional quotients, generalized Taft algebras $T(r,n)$ and small quantum groups $U_q(\mathfrak{sl}_2)$. In the second part of the paper, we shift to the language of tensor categories. Here we consider a quiver path algebra equipped with an action of a Hopf algebra $H$ to be a tensor algebra in the tensor category of representations $H$. Such a tensor algebra is generated by an algebra and bimodule in this tensor category. Our second collection of results describe the corresponding bimodule categories via an equivalence with categories of representations of certain explicitly described quivers with relations.
