$C^*$-代数的群胚模型与 Gelfand 对偶
算子代数
2018-08-13 v7
摘要
我们构造了一大类群胚态射，我们称之为群胚的偏态射，它们诱导极大和极小群胚 -代数的 -态射。我们证明了将群胚对应于其极大（极小）群胚 -代数，以及将偏态射对应于其诱导态射的关联是函子（两者均扩张了 Gelfand 函子）。我们展示了如何将群胚 -代数之间的许多 -态射进行几何可视化。作为应用，我们构造了 Jiang-Su 代数 和 Razak-Jacelon 代数 的整个归纳系统的群胚模型。
引用
@article{arxiv.1804.00967,
title = {Groupoid Models of $C^*$-algebras and Gelfand Duality},
author = {Kyle Austin and Atish Mitra},
journal= {arXiv preprint arXiv:1804.00967},
year = {2018}
}
备注
Based on lots of feedback, we decided to change the title. We also added the case of reduced (or minimal) groupoid $C^*$-algebras. Lastly, we added a subsection (subsection 4.4) which completes the Gelfand duality theorem for commutative $C^*$-algebras will all $*$-morphisms. We updated some of our proofs and gave lots of examples that did not exist in the previous versions