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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Canadian Journal of Mathematics
( Vol. 53 NO.6 / (2001))
Classification of Certain Simple $C^*$-Algebras with Torsion in $K_1$
Jesper Mygind,
Pages. 1223-1308
Abstract We show that the Elliott invariant is a classifying invariant for the class of $C^*$-algebras that are simple unital infinite dimensional inductive limits of finite direct sums of building blocks of the form \
$${ f in C(Bbb{T}) otimes M_n : f(x_i) in M_{d_i}, i=1,2,ldots, N}$$
wehre $x_1, x_2, ldots, x_N in Bbb{T}, d_1, d_2, ldots, d_N$ are integers dividing $n$, and $M_{d_i}$ is embedded unitally into $M_n$. Furthermore we prove exisence and uniqueness theorems for $*$-homomorphisms between such algebras as we identity the range of the invariant.
Contents 1. Introduction
2. Building blocks
3. $K$-theory
4. $KK$-theory
5. The commutator subgroup ofthe unitary group
6. Homomorphisms between building blocks
7. Uniqueness
8. Existence
9. Injective connecting maps
10. Construction of a certain map
11. Main results
12. Range of the invariant
Key words
Mathmatical Subject Classification