Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591273 | Journal of Functional Analysis | 2012 | 20 Pages |
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 K0-ordered groups are isomorphic. Also, using Gong and Dadarlatʼs 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.
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Physical Sciences and Engineering
Mathematics
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