Abstract
Dye proved that the discrete unitary group in a factor determines the algebraic type of the factor. We show that if the unitary groups of two simple unital AH-algebras of slow dimension growth and of real rank zero are isomorphic as abstract groups, then their K 0-ordered groups are isomorphic. Also, using Gong and Dadarlat's classification theorem, we prove that such C *-algebras are isomorphic if and only if their unitary groups are isomorphic as topological groups. For simple, unital purely infinite C *-algebras, we show that two unital Kirchberg algebras are *-isomorphic if and only if their unitary groups are isomorphic as abstract groups.
Original language | English |
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Pages (from-to) | 4711-4730 |
Number of pages | 20 |
Journal | Journal of Functional Analysis |
Volume | 262 |
Issue number | 11 |
DOIs | |
Publication status | Published - Jun 1 2012 |
Keywords
- C -algebras
- K-theory
- Unitary groups
ASJC Scopus subject areas
- Analysis