发表机构
University of Sydney; Victoria University of Wellington; Queen’s University Belfast; MSU-Iligan Institute of Technology（悉尼大学; 惠灵顿维多利亚大学; 贝尔法斯特女王大学; 棉兰老国立理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文引入Cartan逆半群概念，证明$R$-代数存在Cartan逆半群当且仅当同构于扭曲Steinberg代数，扩展了拟Cartan子代数理论。
AI 中文摘要
我们引入了Cartan逆半群的概念，以及在$R$-代数$A$中的（代数）半Cartan子代数，为C*-代数中的Cartan半群和半Cartan子代数提供了一个纯代数的类比。这扩展了拟Cartan子代数的理论，将焦点从指定的子代数转移到指定的子半群。我们的主要结果刻画了扭曲Steinberg代数与Cartan逆半群存在性的关系：我们证明了一个$R$-代数承认一个Cartan逆半群当且仅当它与一个扭曲Steinberg代数同构。此外，当我们的构造应用于一个ample Hausdorff群胚上的扭曲Steinberg代数时，所构造的扭曲自然同构于原始的扭曲。
英文摘要
We introduce the notion of a Cartan inverse semigroup and an (algebraic) semi-Cartan subalgebra in an $R$-algebra A, providing a purely algebraic analogue of Cartan semigroups and semi-Cartan subalgebras in a C*-algebra. This extends the theory of quasi-Cartan subalgebras, shifting the focus from designated subalgebras to designated subsemigroups. Our main result characterises twisted Steinberg algebras in terms of the existence of a Cartan inverse semigroup: we show that an $R$-algebra admits a Cartan inverse semigroup if and only if it is isomorphic to a twisted Steinberg algebra. Moreover, when our construction is applied to a twisted Steinberg algebra over an ample Hausdorff groupoid, the constructed twist is naturally isomorphic to the original one.
Comments14 pages, any feedback is welcome
