On cohomology for product systems

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

75 Downloads (Pure)

Resumé

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.
OriginalsprogEngelsk
TidsskriftBanach Journal of Mathematical Analysis
Vol/bind11
Udgave nummer2
Sider (fra-til)282-294
ISSN1735-8787
DOI
StatusUdgivet - 2017

Fingeraftryk

Product Systems
Cohomology
Cuntz Algebra
Bimodule
Cocycle
Functor
C*-algebra
Hilbert

Citer dette

@article{21b69aa1b67b4a7a868bf9cc382d2b1a,
title = "On cohomology for product systems",
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.",
keywords = "C*-algebra, cohomology, Hilbert bimodule, product system",
author = "Hong, {Jeong Hee} and Son, {Mi Jung} and Wojciech Szymanski",
year = "2017",
doi = "10.1215/17358787-3812500",
language = "English",
volume = "11",
pages = "282--294",
journal = "Banach Journal of Mathematical Analysis",
issn = "1735-8787",
publisher = "Duke University Press",
number = "2",

}

On cohomology for product systems. / Hong, Jeong Hee; Son, Mi Jung; Szymanski, Wojciech.

I: Banach Journal of Mathematical Analysis, Bind 11, Nr. 2, 2017, s. 282-294.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - On cohomology for product systems

AU - Hong, Jeong Hee

AU - Son, Mi Jung

AU - Szymanski, Wojciech

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - C-algebra

KW - cohomology

KW - Hilbert bimodule

KW - product system

U2 - 10.1215/17358787-3812500

DO - 10.1215/17358787-3812500

M3 - Journal article

VL - 11

SP - 282

EP - 294

JO - Banach Journal of Mathematical Analysis

JF - Banach Journal of Mathematical Analysis

SN - 1735-8787

IS - 2

ER -