On cohomology for product systems

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Abstract

A cohomology for product systems of Hilbert bimodules is defined via the Ext functor. For the class of product systems corresponding to irreversible algebraic dynamics, relevant resolutions are found explicitly and it is shown how the underlying product system can be twisted by 2-cocycles. In particular, this process gives rise to cohomological deformations of the C*-algebras associated with the product system. Concrete examples of deformations of the Cuntz's algebra Q_N arising this way are investigated, and we show that they are simple and purely infinite.
Original languageEnglish
JournalBanach Journal of Mathematical Analysis
Volume11
Issue number2
Pages (from-to)282-294
ISSN1735-8787
DOIs
Publication statusPublished - 2017

Keywords

  • C*-algebra
  • cohomology
  • Hilbert bimodule
  • product system

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