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{\Large Department of Mathematics, BGU}

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{\Huge Operator Algebras and Operator Theory}\\[0.2\baselineskip]

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\textbf{On} \emph{Monday, March 11, 2024}
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\textbf{At} \emph{14:00 -- 15:00}
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\textbf{In} \emph{201}

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{\large\scshape Ilan Hirshberg 
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  (BGU)
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will talk about
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{\Large\bfseries Values of Rokhlin dimension for finite group actions\par}
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\textsc{Abstract:}
Finite Rokhlin dimension, a generalization of the Rokhlin property, is a regularity property for actions 
of certain groups on C\emph{-algebras. The main interest in Rokhlin dimension was its use to establish various 
permanence properties: for example, if the C}-algebra acted on has finite nuclear dimension and the action has
finite Rokhlin dimension then the crossed product again has finite nuclear dimension. As such, the main interest in
Rokhlin dimension was to show that it is finite, and not much attention was paid to its actual value. In particular, while
it is known that there are actions with positive finite Rokhlin dimension (that is, have finite Rokhlin dimension but do not
have the Rokhlin property, which corresponds to Rokhlin dimension zero), there were no examples of actions of finite groups
with finite Rokhlin dimension greater than 2. I’ll discuss a recent preprint in which we provide examples of actions of finite groups
on simple AF algebras with arbitrarily large finite Rokhlin dimension. This shows that Rokhlin dimension is not just a tool to establish
regularity results, but is an interesting invariant for group actions, which in a sense measures the complexity of the action.

This is joint work with N. Christopher Phillips.








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