Radius of Comparison and C*-dynamics

Wednesday, February 24, 2021 - 2:00pm to 3:00pm
Location: 
Online via Zoom

Speaker

Ali Asadi-Vasfi
Doctoral student
University of Tehran

Abstract

Let G be a finite group, let A be an infinite-dimensional stably finite simple unital C*-algebra, and let α: G → Aut(A) be an action of G on A which has the weak tracial Rokhlin property. Let Aα be the fixed point algebra. We then prove that: (1) The radius of comparison satisfies rc(Aα ) ≤ rc(A) and rc C ∗ (G, A, α) ≤ 1 card(G) · rc(A). (2) There is an example in which G = Z/2Z, A is a simple unital AH algebra, α has the Rokhlin property, rc(A) > 0, rc(Aα ) = rc(A), and rc(C ∗ (G, A, α)) = 1 2 rc(A). Let G be a finite group, let A be an infinite-dimensional stably finite simple unital C*-algebra, and let α: G → Aut(A) be a tracially strictly approximately inner action of G on A. We then prove that: (1) The radius of comparison satisfies rc(A) ≤ rc C ∗ (G, A, α) . (2) If C ∗ (G, A, α) is simple, then rc(A) ≤ rc C ∗ (G, A, α) ≤ rc(Aα ). (3) For every finite group G and for every η ∈ 0, 1 card(G) , there is a simple separable unital AH algebra A with stable rank one and a strictly approximately inner action α: G → Aut(A) such that α is pointwise outer and rc(A) = rc (C ∗ (G, A, α)) = η. Further, actions of finite groups on many nonclassifiable simple unital C*-algebras cannot simultaneously have the weak tracial Rokhlin property and be tracially strictly approximately inn

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(Please email the organizer John Quigg quigg@asu.edu to be put on the email list if you would like to receive the link to the zoom seminar.)

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