一类正的K_0-群同态的提升

The Lifting of Certain Positive K_0-groups Homomorphisms

设0→I→A与B→0为C＊-代数扩张，其中I为AF-代数，A为有单位元的C＊-代数．设D为一类AF-代数．本文利用投影元的保序提升和K0-群的归纳极限来研究K0（D）到K0（B）的群同态被K0（π）提升的问题．从而得到，如果中为从K0（D）到K0（B）的正的群同态且Ф（[1D]0）=[1B]0，则中可以被K0（π）提升．

Let 0 → I → A →B → 0 be an extension of C＊-algebras, where I is an AF-algebra and A is a unital C＊-algebra. Let D be certain AF-algebra. By the preserving order lifting of projections and the inductive limits of K0-groups, we study the lifting problem of homomorphisms from Ko（D） to Ko（B）. If Ф ： K0（D） → K0（B） is a positive K0-group homomorphism for which Ф（[1D]0） = [1B]0, then Ф can be lifted by K0（π）.