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作用素環セミナー
過去の記録 ～09/19｜次回の予定｜今後の予定 09/20～
| 開催情報 | 月曜日 15:30～17:00 数理科学研究科棟(駒場) 号室 |
|---|---|
| 担当者 | 松井 宏樹、木田 良才、河東 泰之 |
| セミナーURL | https://sites.google.com/view/hirokimatui/tokyo-seminar |
2026年11月30日(月)
15:30-17:00 数理科学研究科棟(駒場) 126 号室
紅村 冬大 氏 (九州工業大学)
Cartan-preserving *-automorphism groups: realization and obstructions for compact abelian groups
紅村 冬大 氏 (九州工業大学)
Cartan-preserving *-automorphism groups: realization and obstructions for compact abelian groups
[ 講演概要 ]
In this talk, 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 if the fixed point subalgebras are prime. As an application, we establish the existence of inequivalent Cartan subalgebras for Kirchberg algebras arising from expansive effective groupoids.
In this talk, 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 if the fixed point subalgebras are prime. As an application, we establish the existence of inequivalent Cartan subalgebras for Kirchberg algebras arising from expansive effective groupoids.
