C(X)A上的自同构群

Automorphism Group on the C(X)A

本文研究了连续函数代数C（X）与某个C*-代数A的张量积C（X）A的自同构群．当A是有单位元且具有平凡中心的C*-代数时，本文完全刻划了C（X）A的自同构群．利用AF-代数的K-理论，本文还刻划了当X是全不连通的紧致Hausdorff空间时，C（X）与紧算子理想的张量积的自同构群．

The paper studied the automorphism on the tensor product C(X)A of the continuously function algebra and some C*-algebra. When A is a unita1 C*-algebra with trivial center, the paper characterized completely the automorphism group on the C(X)A. By using K-theory of AF-algebra, the paper characterized the automorphism group on the tensor product of the C(X) and the compact ideal when X is a tottaly disconnected compact Hausdoof space.