Open Access
April 2017 On cohomology for product systems
Jeong Hee Hong, Mi Jung Son, Wojciech Szymański
Banach J. Math. Anal. 11(2): 282-294 (April 2017). DOI: 10.1215/17358787-3812500


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 QN arising this way are investigated, and we show that they are simple and purely infinite.


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Jeong Hee Hong. Mi Jung Son. Wojciech Szymański. "On cohomology for product systems." Banach J. Math. Anal. 11 (2) 282 - 294, April 2017.


Received: 7 February 2016; Accepted: 11 May 2016; Published: April 2017
First available in Project Euclid: 19 January 2017

zbMATH: 1372.46041
MathSciNet: MR3598745
Digital Object Identifier: 10.1215/17358787-3812500

Primary: 46L08
Secondary: 18G10 , 46L65

Keywords: $C^{*}$-algebra , Cohomology , Hilbert bimodule , product system

Rights: Copyright © 2017 Tusi Mathematical Research Group

Vol.11 • No. 2 • April 2017
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