AI 中文总结
研究 C*-代数中保卡坦子代数的自同构群，通过扭曲 étale 群胚描述，得到相关定理类似物。研究卡坦固定自同构群，证明 UCT 基尔希贝格代数的相关性质，及扩张有效群胚产生的 C*-代数的性质，还给出不等价卡坦子代数存在性。
AI 中文摘要
本文研究了 C*-代数中保卡坦子代数的自同构群。首先，我们根据扭曲 étale 群胚的自同构和 1-上循环来描述这些群。由此，我们得到了冯·诺依曼代数中保卡坦自同构的费尔德曼和摩尔定理的 C*-代数类似物。接着研究了卡坦固定自同构群。证明了每个 UCT 基尔希贝格代数都有一个卡坦子代数，其卡坦固定自同构群包含每个第二可数紧致阿贝尔群。相反，对于由扩张有效群胚产生的 C*-代数，紧致卡坦固定自同构群的庞特里亚金对偶必须是有限生成的。作为应用，我们证明了由扩张有效群胚产生的基尔希贝格代数中存在不等价的卡坦子代数。
英文摘要
In this paper, we investigate automorphism groups preserving Cartan subalgebras of C*-algebras. First, we describe these groups in terms of automorphisms and 1-cocycles of twisted étale groupoids. As a consequence, we obtain a C*-algebraic analogue of a theorem of Feldman and Moore on Cartan-preserving automorphisms of von Neumann algebras. We then study Cartan-fixing automorphism groups. We show that every UCT Kirchberg algebra admits a Cartan subalgebra whose Cartan-fixing automorphism group contains every second countable compact abelian group. In contrast, for C*-algebras arising from expansive effective groupoids, we prove that compact Cartan-fixing automorphism groups must have finitely generated Pontryagin duals. As an application, we establish the existence of inequivalent Cartan subalgebras for Kirchberg algebras arising from expansive effective groupoids.
Comments38 pages
