Text only print
Full screen print
Operator Algebra Seminars
Seminar information archive ～09/19｜Next seminar｜Future seminars 09/20～
| Date, time & place | Monday 15:30 - 17:00 Room # (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | MATUI Hiroki, KIDA Yoshikata, KAWAHIGASHI Yasuyuki |
2026/11/30
15:30-17:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Fuyuta Komura (Kyushu Institute of Technology)
Cartan-preserving *-automorphism groups: realization and obstructions for compact abelian groups
Fuyuta Komura (Kyushu Institute of Technology)
Cartan-preserving *-automorphism groups: realization and obstructions for compact abelian groups
[ Abstract ]
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.
