Finite group actions on C*-algebras with the Rohlin property, I

By Masaki Izumi. 2004

200 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/940c967e437b4f934f7c2b07296da35e2cc74952

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In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

Rokhlin actions and self-absorbing C*-algebras (2005, background): “There are many examples of C∗-algebras with Rokhlin actions; see [Izumi 2004a; 2004b] for the finite group case and [Kishimoto 2000; 2001] for the case where G = Z or R. Rokhlin flows and a number of striking applications to the theory of purely infinite C∗-algebras have been studied in [Kishimoto…”
Q-system completion for C⁎ 2-categories (2021, unknown): “Recently there has been significant interest in classifying actions of groups and unitary tensor categories on (unital) C ∗ -algebras [Izu04, Sza19, BS17, IM19a, IM19b] [Jon21a, EGP21, Ara].”
The tracial Rokhlin property for actions of finite groups on C*-algebras (2006, background): “8 of [10], showing that an action is tracially approximately representable if and only if the dual action has the tracial Rokhlin property, and similarly with the action and its dual exchanged.”
Freeness of actions of finite groups on C*-algebras (2009, background): “1 of [25] asks for mutually orthogonal projections eg ∈ A∞ for g ∈ G such that ∑ g∈G eg = 1 and such that (α∞)g(eh) = egh for all g, h ∈ G.”
Crossed products by finite group actions with the Rokhlin property (2007, methodology): “The Rokhlin property is as in Definition 3.1 of [ 16 ]; we reproduce here the equivalent form given in Definition 1.1 of [28].”
Finite cyclic group actions with the tracial Rokhlin property (2006, methodology): “The definition of [ 11 ] is actually stated in terms of central sequences, but it is equivalent to our definition by Lemma 3.1 of [26].”
Every simple higher dimensional noncommutative torus is an AT algebra (2006, background): “It is not possible to substitute the Rokhlin property of [15] and [16] in this argument.”
Rokhlin dimension for compact group actions (2014, methodology): “) It is well known that μ (and any tensor product of it with any other action) has the Rokhlin property; see [16].”
Sequentially split ∗-homomorphisms between C*-algebras (2015, background): “this viewpoint for Rokhlin actions some more, we prove a K-theory formula for the ﬁxed point algebra of a Rokhlin action, generalizing such a K-theory formula for ﬁnite groups established by Izumi in [25]. Another one of Izumi’s observations from [25] is that for ﬁnite abelian groups, Rokhlin action”
Strongly self-absorbing *-dynamical systems (2015, methodology): “For ﬁnite group actions, Izumi has alluded to special cases of such an absorption theorem in [15].”
Rokhlin dimension for actions of residually finite groups (2014, background): “Then Izumi started his pioneering work on finite group actions with the Rokhlin property (see [30, 31]).”