Journal of the Ramanujan Mathematical Society

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A Complete Classification of Limits of Splitting Interval Algebras with the Ideal Property


Affiliations
1 College of Mathematics Hebei Normal University Shijiazhuang, 050016, Hebei, China
2 Department of Mathematics, University of Puerto Rico, Rio Piedras Campus, P.O.Box 70377, San Juan, Puerto Rico, United States
     

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Let A = lim (An, φn,m) be an inductive limit C∗-algebra with An = ⨁kni =1 Ai n with the Ai n splitting interval algebras. Suppose that A has the ideal property: each closed two-sided ideal is generated (as an ideal) by projections in the ideal. In this article, we will show that the scaled ordered K0 group and the ordered vector spaces AffT(eAe) with e a projection together with the natural maps between them are complete invariants for the classification of this class of C∗-algebras.
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  • A Complete Classification of Limits of Splitting Interval Algebras with the Ideal Property

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Authors

Chunlan Jiang
College of Mathematics Hebei Normal University Shijiazhuang, 050016, Hebei, China
Kun Wang
Department of Mathematics, University of Puerto Rico, Rio Piedras Campus, P.O.Box 70377, San Juan, Puerto Rico, United States

Abstract


Let A = lim (An, φn,m) be an inductive limit C∗-algebra with An = ⨁kni =1 Ai n with the Ai n splitting interval algebras. Suppose that A has the ideal property: each closed two-sided ideal is generated (as an ideal) by projections in the ideal. In this article, we will show that the scaled ordered K0 group and the ordered vector spaces AffT(eAe) with e a projection together with the natural maps between them are complete invariants for the classification of this class of C∗-algebras.