论文标题
c* - 代数及其K理论的同态
Homomorphisms of C*-algebras and their K-theory
论文作者
论文摘要
令$ a $和$ b $为c*-algebras，$φ\ colon a \ to b $是$*$ - 同构。我们讨论了诱导地图$ \ mathrm {k} _ {0}（φ）\ colon \ mathrm {k} _ {0}（a）\ to \ mathrm {k Mathrm {k} _ {0} _ {0} _ {0} _（b）$的属性和（共同）图像的属性。尤其是，我们对共同形象不含扭力感兴趣，并表明当$ a $ a和$ b $是可交值和Unital时，$ b $具有真正的排名零，而$φ$是Unital and Impotive的。我们还表明，如果$ \ mathrm {k} _ {0}（φ）$是iNjective，并且$ a $具有稳定的排名第一和实际等级零。
Let $A$ and $B$ be C*-algebras and $φ\colon A\to B$ be a $*$-homomorphism. We discuss the properties of the kernel and (co-)image of the induced map $\mathrm{K}_{0}(φ)\colon \mathrm{K}_{0}(A) \to \mathrm{K}_{0}(B)$ on the level of K-theory. In particular, we are interested in the case that the co-image is torsion free, and show that it holds when $A$ and $ B $ are commutative and unital, $B$ has real rank zero, and $φ$ is unital and injective. We also show that $ A$ is embeddable in $B$ if $ \mathrm{K}_{0}(φ)$ is injective and $A$ has stable rank one and real rank zero.
