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

2007/05/10 by Marius Dădărlat, Wilhelm Winter, Dadarlat, Marius +1 · 1 citation
Mathematics · #46L05 #47L40 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.0705.1497

openalex publication_date 2007/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose A is a separable unital C(X)-algebra each fibre of which is isomorphic to the same strongly self-absorbing and K₁-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.

Cited by

• Continuous fields of properly infinite C*-algebras

Related

• Strongly self-absorbing C*-algebras
• On the KK-theory of strongly self-absorbing C*-algebras
• C₀(X)-algebras, stability and strongly self-absorbing C*-algebras
• Continuous fields of properly infinite C*-algebras
• Continuous families of properly infinite C*-algebras