Suslin A A, Wodzicki M
Leningrad Branch of the Steklov Mathematical Institute, Leningrad, U.S.S.R.
Proc Natl Acad Sci U S A. 1990 Dec 15;87(24):9582-4. doi: 10.1073/pnas.87.24.9582.
We prove that the property of excision in algebraic K-theory is for a Q-algebra A equivalent to the H-unitality of the latter. Our excision theorem, in particular, implies Karoubi's conjecture on the equality of algebraic and topological K-theory groups of stable C*-algebras. It also allows us to identify the algebraic K-theory of the symbol map in the theory of pseudodifferential operators.
我们证明，对于一个有理数域(\mathbb{Q})上的代数(A)，代数(K)-理论中的切除性质等同于该代数的(H)-单位性。特别地，我们的切除定理蕴含了卡鲁比关于稳定(C^*)-代数的代数(K)-理论群与拓扑(K)-理论群相等的猜想。它还使我们能够在伪微分算子理论中确定符号映射的代数(K)-理论。
