A Complete Invariant forADAlgebras with Real Rank Zero and Bounded Torsion inK1
✍ Scribed by Søren Eilers
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 972 KB
- Volume
- 139
- Category
- Article
- ISSN
- 0022-1236
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✦ Synopsis
For each integer p>1, we consider an algebraic invariant for C*-algebras. The invariant consists of K 0 , K 1 , the K 0 -group with ZÂp coefficients, the order structures these groups possess, and the natural maps between the three groups. We prove that this invariant is complete for the class of AD algebras of real rank zero if p annihilates every torsion element of K 1 . The AD algebras are C*-algebras which are inductive limits of finite direct sums of C*-algebras of continuous matrix-valued functions over the circle, or over the interval, where in the interval case we require that the value over the endpoints is a scalar multiple of the unit matrix. Examples show that the condition on the torsion in K 1 is necessary when only one mod p K 0 -group is considered. Applying a theorem of Da$ da$ rlat, the result also applies to a subclass of the AH algebras.