论文标题
量子逆半群
Quantum Inverse Semigroups
论文作者
论文摘要
在这项工作中，引入了量子反向半群的概念，作为反向半群的线性化概括。除了一个反向半群的代数（这是量子反向半群的自然示例）之外，这种新结构的其他几个示例也在不同的情况下呈现，这些示例与Hopf代数，弱Hopf代数，部分动作和HOPF类别有关。最后，在交换基础代数上定义了局部两种序列的普遍概念，从而产生了与Hopf代数相关的量子逆半群的新示例，而逆半群也与Hopf代数相关的含义是逆半群与类别型相关。
In this work, the notion of a quantum inverse semigroup is introduced as a linearized generalization of inverse semigroups. Beyond the algebra of an inverse semigroup, which is the natural example of a quantum inverse semigroup, several other examples of this new structure are presented in different contexts, those are related to Hopf algebras, weak Hopf algebras, partial actions and Hopf categories. Finally, a generalized notion of local bisections are defined for commutative Hopf algebroids over a commutative base algebra giving rise to new examples of quantum inverse semigroups associated to Hopf algebroids in the same sense that inverse semigroups are related to groupoids.
