Trivialization of 𝒞(X)-algebras with strongly self-absorbing fibres
Bulletin de la Société Mathématique de France, Volume 136 (2008) no. 4, p. 575-606

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.

Soit A une 𝒞(X)-algèbre séparable unital dont chaque fibre est isomorphe à une même C * -algèbre 𝒟 K 1 -injective et fortement auto-absorbante. Nous montrons que si l’espace compact et Hausdorff X est de dimension finie, alors A et 𝒞(X)𝒟 sont isomorphes en tant que 𝒞(X)-algèbres. Ce resultat est connu pour ne pas s’étendre au cas des espaces de dimension infinie.

DOI : https://doi.org/10.24033/bsmf.2567
Classification:  46L05,  47L40
Keywords: strongly self-absorbing C * -algebra, asymptotic unitary equivalence, continuous field of C * -algebras
@article{BSMF_2008__136_4_575_0,
     author = {Dadarlat, Marius and Winter, Wilhelm},
     title = {Trivialization of $\mathcal {C}(X)$-algebras with strongly self-absorbing fibres},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {136},
     number = {4},
     year = {2008},
     pages = {575-606},
     doi = {10.24033/bsmf.2567},
     zbl = {1170.46051},
     mrnumber = {2443037},
     language = {en},
     url = {http://www.numdam.org/item/BSMF_2008__136_4_575_0}
}
Dadarlat, Marius; Winter, Wilhelm. Trivialization of $\mathcal {C}(X)$-algebras with strongly self-absorbing fibres. Bulletin de la Société Mathématique de France, Volume 136 (2008) no. 4, pp. 575-606. doi : 10.24033/bsmf.2567. http://www.numdam.org/item/BSMF_2008__136_4_575_0/

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