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

Abstract

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 $C^{\ast }$-algebra $D$. We show that $A$ and $C(X)\otimes D$ 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.

27 pages