Rokhlin dimension for compact group actions

By Eusebio Gardella. 2014

50 citations recorded by the source corpus.

We introduce and systematically study the notion of Rokhlin dimension (with and without commuting towers) for compact group actions on $C^*$-algebras. This notion generalizes the one introduced by Hirshberg, Winter and Zacharias for finite groups, and contains the Rokhlin property as the zero dimensional case. We show, by means of an example, that commuting towers cannot always be arranged, even in the absence of $K$-theoretic obstructions. For a compact Lie group action on a compact Hausdorff space, freeness is equivalent to finite Rokhlin dimension of the induced action. We compare the notion of finite Rokhlin dimension to other existing definitions of noncommutative freeness for compact group actions. We obtain further $K$-theoretic obstructions to having an action of a non-finite compact Lie group with finite Rokhlin dimension with commuting towers, and use them to confirm a conjecture of Phillips.

Subfields: Algebra and Number Theory, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/379bfc2fcc67fecd1bab0073458274cc31f67a70

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In Algebra and Number Theory

  1. G'abor Szab'o
  2. Jianchao Wu
  3. J. Zacharias
  4. W. Winter
  5. Eusebio Gardella

In Mathematical Physics

  1. G'abor Szab'o
  2. Jianchao Wu
  3. J. Zacharias
  4. W. Winter
  5. David Kerr
  6. Eusebio Gardella
  7. Aaron Tikuisis

In Statistical and Nonlinear Physics

  1. G'abor Szab'o
  2. Jianchao Wu
  3. J. Zacharias
  4. W. Winter

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