Trivialization of 𝒞 ( X ) -algebras with strongly self-absorbing fibres

Marius Dadarlat; Wilhelm Winter

Bulletin de la Société Mathématique de France (2008)

  • Volume: 136, Issue: 4, page 575-606
  • ISSN: 0037-9484

Abstract

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Suppose A is a separable unital 𝒞 ( X ) -algebra each fibre of which is isomorphic to the same strongly self-absorbing and K 1 -injective C * -algebra 𝒟 . We show that A and 𝒞 ( X ) ⊗ 𝒟 are isomorphic as 𝒞 ( X ) -algebras provided the compact Hausdorff space X is finite-dimensional. This statement is known not to extend to the infinite-dimensional case.

How to cite

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Dadarlat, Marius, and Winter, Wilhelm. "Trivialization of $\mathcal {C}(X)$-algebras with strongly self-absorbing fibres." Bulletin de la Société Mathématique de France 136.4 (2008): 575-606. <http://eudml.org/doc/272309>.

@article{Dadarlat2008,
abstract = {Suppose $A$ is a separable unital $\mathcal \{C\}(X)$-algebra each fibre of which is isomorphic to the same strongly self-absorbing and $K_\{1\}$-injective $C^\{*\}$-algebra $\mathcal \{D\}$. We show that $A$ and $\mathcal \{C\}(X) \otimes \mathcal \{D\}$ are isomorphic as $\mathcal \{C\}(X)$-algebras provided the compact Hausdorff space $X$ is finite-dimensional. This statement is known not to extend to the infinite-dimensional case.},
author = {Dadarlat, Marius, Winter, Wilhelm},
journal = {Bulletin de la Société Mathématique de France},
keywords = {strongly self-absorbing $C^*$-algebra; asymptotic unitary equivalence; continuous field of $C^\{*\}$-algebras},
language = {eng},
number = {4},
pages = {575-606},
publisher = {Société mathématique de France},
title = {Trivialization of $\mathcal \{C\}(X)$-algebras with strongly self-absorbing fibres},
url = {http://eudml.org/doc/272309},
volume = {136},
year = {2008},
}

TY - JOUR
AU - Dadarlat, Marius
AU - Winter, Wilhelm
TI - Trivialization of $\mathcal {C}(X)$-algebras with strongly self-absorbing fibres
JO - Bulletin de la Société Mathématique de France
PY - 2008
PB - Société mathématique de France
VL - 136
IS - 4
SP - 575
EP - 606
AB - Suppose $A$ is a separable unital $\mathcal {C}(X)$-algebra each fibre of which is isomorphic to the same strongly self-absorbing and $K_{1}$-injective $C^{*}$-algebra $\mathcal {D}$. We show that $A$ and $\mathcal {C}(X) \otimes \mathcal {D}$ are isomorphic as $\mathcal {C}(X)$-algebras provided the compact Hausdorff space $X$ is finite-dimensional. This statement is known not to extend to the infinite-dimensional case.
LA - eng
KW - strongly self-absorbing $C^*$-algebra; asymptotic unitary equivalence; continuous field of $C^{*}$-algebras
UR - http://eudml.org/doc/272309
ER -

References

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  5. [5] M. Dadarlat & W. Winter – « On the K K -theory of strongly self-absorbing C * -algebras », preprint, arXiv:0704.0583, to appear in Math. Scand., 2007. Zbl1170.46065MR2498373
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  12. [12] A. S. Toms & W. Winter – « Strongly self-absorbing C * -algebras », Trans. Amer. Math. Soc.359 (2007), p. 3999–4029. Zbl1120.46046MR2302521
  13. [13] W. Winter – « Localizing the Elliott conjecture at strongly self-absorbing C * -algebras », preprint, arXiv:0708.0283, 2007. MR2302521
  14. [14] —, « Simple C * -algebras with locally finite decomposition rank », J. Funct. Anal.243 (2007), p. 394–425. Zbl1121.46047MR2289694

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