Symmetry, Integrability and Geometry: Methods and Applications
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



SIGMA:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 082, 21 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.082
(Mi sigma1619)
 

This article is cited in 4 scientific papers (total in 4 papers)

On the Unbounded Picture of $KK$-Theory

Jens Kaad

Department of Mathematics and Computer Science, The University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
Full-text PDF (418 kB) Citations (4)
References:
Abstract: In the founding paper on unbounded $KK$-theory it was established by Baaj and Julg that the bounded transform, which associates a class in $KK$-theory to any unbounded Kasparov module, is a surjective homomorphism (under a separability assumption). In this paper, we provide an equivalence relation on unbounded Kasparov modules and we thereby describe the kernel of the bounded transform. This allows us to introduce a notion of topological unbounded $KK$-theory, which becomes isomorphic to $KK$-theory via the bounded transform. The equivalence relation is formulated entirely at the level of unbounded Kasparov modules and consists of homotopies together with an extra degeneracy condition. Our degenerate unbounded Kasparov modules are called spectrally decomposable since they admit a decomposition into a part with positive spectrum and a part with negative spectrum.
Keywords: $KK$-theory, unbounded $KK$-theory, equivalence relations, bounded transform.
Funding agency Grant number
Independent Research Fund Denmark 7014-00145B
The author was partially supported by the DFF-Research Project 2 “Automorphisms and Invariants of Operator Algebras”, no. 7014-00145B.
Received: October 22, 2019; in final form August 5, 2020; Published online August 22, 2020
Bibliographic databases:
Document Type: Article
MSC: 19K35, 58B34
Language: English
Citation: Jens Kaad, “On the Unbounded Picture of $KK$-Theory”, SIGMA, 16 (2020), 082, 21 pp.
Citation in format AMSBIB
\Bibitem{Kaa20}
\by Jens~Kaad
\paper On the Unbounded Picture of $KK$-Theory
\jour SIGMA
\yr 2020
\vol 16
\papernumber 082
\totalpages 21
\mathnet{http://mi.mathnet.ru/sigma1619}
\crossref{https://doi.org/10.3842/SIGMA.2020.082}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000564519600001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85093904358}
Linking options:
  • https://www.mathnet.ru/eng/sigma1619
  • https://www.mathnet.ru/eng/sigma/v16/p82
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024