论文标题
通用量子半族类型
Universal quantum semigroupoids
论文作者
论文摘要
我们介绍了通用量子线性半族类（UQSGD）的概念，该概念是一个弱的双子，它在（不一定连接的）分级代数$ a $上均普遍保存分级时共同划分。我们将注意力限制在具有交换基础的代数结构上，以使所研究的UQSGD面对代数（由于Hayashi）。 UQSGD结构概括了Manin在1988年引入的通用量子线性半群，该量子是在保留分级的同时，在连接的分级代数上共同划分的代数。我们的主要结果是，当$ a $是有限箭袋$ q $的路径代数$ \ bbbk q $时，此处介绍的各种UQSGD中的每个UQSGD都与附加到$ Q $的面部代数同构。还研究了前体代数的UQSGD和附着在颤抖的其他代数的UQSGD。
We introduce the concept of a universal quantum linear semigroupoid (UQSGd), which is a weak bialgebra that coacts on a (not necessarily connected) graded algebra $A$ universally while preserving grading. We restrict our attention to algebraic structures with a commutative base so that the UQSGds under investigation are face algebras (due to Hayashi). The UQSGd construction generalizes the universal quantum linear semigroups introduced by Manin in 1988, which are bialgebras that coact on a connected graded algebra universally while preserving grading. Our main result is that when $A$ is the path algebra $\Bbbk Q$ of a finite quiver $Q$, each of the various UQSGds introduced here is isomorphic to the face algebra attached to $Q$. The UQSGds of preprojective algebras and of other algebras attached to quivers are also investigated.
