Morphisms of Extensions of C*-algebras: Pushing Forward the Busby Invariant

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Standard

Morphisms of Extensions of C*-algebras: Pushing Forward the Busby Invariant. / Eilers, Søren; Loring, Terry A.; Pedersen, Gert Kjærgård.

I: Advances in Mathematics, Bind 147, Nr. 1, 1999, s. 74-109.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Eilers, S, Loring, TA & Pedersen, GK 1999, 'Morphisms of Extensions of C*-algebras: Pushing Forward the Busby Invariant', Advances in Mathematics, bind 147, nr. 1, s. 74-109. https://doi.org/10.1006/aima.1999.1834

APA

Eilers, S., Loring, T. A., & Pedersen, G. K. (1999). Morphisms of Extensions of C*-algebras: Pushing Forward the Busby Invariant. Advances in Mathematics, 147(1), 74-109. https://doi.org/10.1006/aima.1999.1834

Vancouver

Eilers S, Loring TA, Pedersen GK. Morphisms of Extensions of C*-algebras: Pushing Forward the Busby Invariant. Advances in Mathematics. 1999;147(1):74-109. https://doi.org/10.1006/aima.1999.1834

Author

Eilers, Søren ; Loring, Terry A. ; Pedersen, Gert Kjærgård. / Morphisms of Extensions of C*-algebras: Pushing Forward the Busby Invariant. I: Advances in Mathematics. 1999 ; Bind 147, Nr. 1. s. 74-109.

Bibtex

@article{432c804074c911dbbee902004c4f4f50,
title = "Morphisms of Extensions of C*-algebras: Pushing Forward the Busby Invariant",
abstract = "We study completions of diagrams of extensions of C*-algebras in which all three C*-algebras in one of the rows and either the ideal or the quotient in the other are given, along with the three morphisms between them. We find universal solutions to all four of these problems under restrictions of varying severity, on the given vertical maps and describe the solutions in terms of push-outs and pull-backs of certain diagrams. Our characterization of the universal solution to one of the diagrams yields a concrete description of various amalgamated free products. This leads to new results about the K-theory of amalgamated free products, verifying the Cuntz conjecture in certain cases. We also obtain new results about extensions of matricial fieldC*-algebras, verifying partially a conjecture of Blackadar and Kirchberg. Finally, we show that almost commuting unitary matrices can be uniformly approximated by commuting unitaries when an index obstruction vanishes.",
author = "S{\o}ren Eilers and Loring, {Terry A.} and Pedersen, {Gert Kj{\ae}rg{\aa}rd}",
year = "1999",
doi = "10.1006/aima.1999.1834",
language = "English",
volume = "147",
pages = "74--109",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press",
number = "1",

}

RIS

TY - JOUR

T1 - Morphisms of Extensions of C*-algebras: Pushing Forward the Busby Invariant

AU - Eilers, Søren

AU - Loring, Terry A.

AU - Pedersen, Gert Kjærgård

PY - 1999

Y1 - 1999

N2 - We study completions of diagrams of extensions of C*-algebras in which all three C*-algebras in one of the rows and either the ideal or the quotient in the other are given, along with the three morphisms between them. We find universal solutions to all four of these problems under restrictions of varying severity, on the given vertical maps and describe the solutions in terms of push-outs and pull-backs of certain diagrams. Our characterization of the universal solution to one of the diagrams yields a concrete description of various amalgamated free products. This leads to new results about the K-theory of amalgamated free products, verifying the Cuntz conjecture in certain cases. We also obtain new results about extensions of matricial fieldC*-algebras, verifying partially a conjecture of Blackadar and Kirchberg. Finally, we show that almost commuting unitary matrices can be uniformly approximated by commuting unitaries when an index obstruction vanishes.

AB - We study completions of diagrams of extensions of C*-algebras in which all three C*-algebras in one of the rows and either the ideal or the quotient in the other are given, along with the three morphisms between them. We find universal solutions to all four of these problems under restrictions of varying severity, on the given vertical maps and describe the solutions in terms of push-outs and pull-backs of certain diagrams. Our characterization of the universal solution to one of the diagrams yields a concrete description of various amalgamated free products. This leads to new results about the K-theory of amalgamated free products, verifying the Cuntz conjecture in certain cases. We also obtain new results about extensions of matricial fieldC*-algebras, verifying partially a conjecture of Blackadar and Kirchberg. Finally, we show that almost commuting unitary matrices can be uniformly approximated by commuting unitaries when an index obstruction vanishes.

U2 - 10.1006/aima.1999.1834

DO - 10.1006/aima.1999.1834

M3 - Journal article

VL - 147

SP - 74

EP - 109

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 1

ER -

ID: 196849