论文标题
网络上的准隔离
Quasi-semilattices on networks
论文作者
论文摘要
本文介绍了网络的张量表示，这里的张量是网络的原始结构。鉴于张量链，定义了张量集的两个二进制操作：链添加和还原。基于还原操作，给出了网络子网的张链链表示，并证明网络的所有连接子网络（此处是指由原始结构生成的张链链）形成了Quasi-semilattice，相对于还原而言，即降低，即\ it网络Quasi quasi quasi quasi-semilattices}。在这里，准隔离是指具有责任感且不满足关联法的代数系统。然后，我们讨论了网络准间隙的子代理结构，以两个等效关系$σ$和$δ$。 $δ$是一致的。每个$δ$ - 类都相对于减少的半层次形成了一个半静脉，即屈服的交换性半群，每个$δ$ - 类也具有最大元素和最小元素的订单结构。在这里，最小元素对应于图理论中的生成树。最后，我们讨论了三个路径代数：图形逆半群，Leavitt Path代数和Cuntz-Krieger图$ C^*$ - 代数是根据张量相对于链条添加的。
This paper introduces the tensor representation of a network, here tensors are the primitive structures of the network. In view of tensor chains, two binary operations on tensor sets are defined: chain addition and reducing. Based on the reducing operation, the tensor chain representation of subnetworks of a network is given, and it is proved that all connected subnetworks of a network (here refers to the tensor chain generated by primitive structures) form a quasi-semilattice with respect to reducing, namely {\it network quasi-semilattices}. Here, quasi-semilattices refer to algebraic systems that are idempotent commutative and do not satisfy the association law. Then, we discuss the subalgebra structures of the network quasi-semilattice in terms of two equivalent relations $σ$ and $δ$. $δ$ is a congruence. Each $δ$-class forms a semilattice with respect to reducing, that is, an idempotent commutative semigroup, and also each $δ$-class has an order structure with the maximum element and minimum elements. Here, the minimum elements correspond to the spanning tree in graph theory. Finally, we discuss how three path algebras: graph inverse semigroups, Leavitt path algebra and Cuntz-Krieger graph $C^*$-algebra are constructed in terms of tensors with respect to chain-addition.
