Analysis Seminar
Title:Invariant Subalgebras of the reduced group C ∗ -algebras
Speaker:Tattwamasi Amrutam （Institute of Mathematics of the Polish Academy of Sciences）
Time: Wednesday, May 28, 2025, 16:00-17:30 (UTC+8)
Venue: Gewu Building, Room 315
Zoom ID: 976 1746 7912 (Password: 971230)
Link:https://zoom.us/j/97617467912?pwd=lzTsNI4eE3SYRaAzusNAxfQd3vabHf.1
Abstract :
Let Γ be a countable discrete group. Associated with it is the reduced group C ∗ -algebra Cr ∗ (Γ) and the group von Neumann algebra L(Γ). It is interesting to ask which group properties are reflected at the group von Neumann algebra or reduced group C ∗ -algebra level. We say that Γ has C ∗ -invariant subalgebra rigidity property (C ∗ -ISR property) if every invariant C ∗ -subalgebra A ≤ Cr ∗ (Γ) is of the form Cr ∗ (N) for some normal subgroup N ◁ Γ.
In this talk, we shall show that there is a significant class of groups Γ for which the only invariant C ∗ - subalgebras inside Cr ∗ (Γ) come from the normal subgroups including all torsion-free non-amenable cylindrically hyperbolic groups and a finite product of such groups; in particular, they satisfy the C ∗ -ISR property. We shall also discuss the implications for infinite groups satisfying the C ∗ -ISR property in that they are either C ∗ -simple or simple amenable.
This is based on the following joint work with Yongle Jiang.
