Sequentially split ∗-homomorphisms between C*-algebras

Selçuk Barlak, Gabor Szabo

Research output: Contribution to journalArticle

14 Citations (Scopus)
5 Downloads (Pure)

Abstract

We define and examine sequentially split ∗-homomorphisms between C*-algebras and C*-dynamical systems. For a ∗-homomorphism, the property of being sequentially split can be regarded as an approximate weakening of being a split-injective inclusion of C*-algebras. We show for a sequentially split ∗-homomorphism that a multitude of C*-algebraic approximation properties pass from the target algebra to the domain algebra, including virtually all important approximation properties currently used in the classification theory of C*-algebras. We also discuss various settings in which sequentially split ∗-homomorphisms arise naturally from context. One particular class of examples arises from compact group actions with the Rokhlin property. This allows us to recover and extend the presently known permanence properties of Rokhlin actions with a unified conceptual approach and a simple proof. Moreover, this perspective allows us to obtain new results about such actions, such as a generalization of Izumi’s original KK-theory formula for the fixed point algebra, or duality between the Rokhlin property and approximate representability.
Original languageEnglish
Article number1650105
Number of pages48
JournalInternational Journal of Mathematics
Volume27
Issue number13
Early online date15 Nov 2016
DOIs
Publication statusPublished - Dec 2016

Keywords

  • Inclusions of C∗-algebras
  • classification of C∗-algebras
  • classification of C∗-dynamical systems
  • Rokhlin property

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