Polycyclic monoids and their generalisations
Polycyclic monoids and their generalisations
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多环幺半群及其推广
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发表时间：
2011
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通讯作者：
David G. Jones
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作者：
David G. Jones
本文分为两个部分。第一个是受Bratteli和Jorgensen的专著的启发。我们研究任意的，不一定传递，强作用的多环逆幺半群Pn。我们得到了一些新的结果，关于强作用的P2在Z上的选择一个正奇数p。我们表明，该表示的结构可以解释通过研究的数字1 p，2 p，. . .，p−1 p .我们还概括了正自共轭子幺半群的Pn和同余之间的连接的自由幺半群由Meakin和萨皮尔开发。第二部分可以看作是第一部分的概括。图逆半群是多圈逆幺半群的推广，在C-代数理论中起着重要的作用。我们提供了一个抽象的表征图逆半群，并显示他们如何可能完成，以形成我们所谓的Cuntz-Krieger半群的图-这个半群，然后半群模拟的莱维特路径代数的图。我们再次概括的连接米金和萨皮尔这一次某些子半群的图形逆半群和同余的自由图。
This thesis can be split into two parts. The first was inspired by a monograph by Bratteli and Jorgensen. We study arbitrary, not necessarily transitive, strong actions of polycyclic inverse monoids Pn. We obtain some new results concerning the strong actions of P2 on Z determined by the choice of one positive odd number p. We show that the structure of the representation can be explained by studying the binary representations of the numbers 1 p , 2 p , . . . , p−1 p . We also generalise the connection between the positively self conjugate submonoids of Pn and congruences on the free monoid An developed by Meakin and Sapir. The second part can be seen as a generalisation of the first. Graph inverse semigroups generalise the polycyclic inverse monoids and play an important role in the theory of C∗-algebras. We provide an abstract characterisation of graph inverse semigroups and show how they may be completed to form what we call the Cuntz-Krieger semigroup of the graph — this semigroup is then the semigroup analogue of the Leavitt path algebra of the graph. We again generalise the connection of Meakin and Sapir this time to certain subsemigroups of the graph inverse semigroup and congruences on the free graph.