TY - JOUR
T1 - Unitary groups as a complete invariant
AU - Al-Rawashdeh, Ahmed
AU - Booth, Andrew
AU - Giordano, Thierry
N1 - Funding Information:
* Corresponding author. Fax: +971 3 7671291. E-mail addresses: [email protected] (A. Al-Rawashdeh), [email protected] (T. Giordano). 1 Partially supported by Research Affairs at UAEU, 1498-02-01-10. 2 Partially supported by NSERC, Canada.
PY - 2012/6/1
Y1 - 2012/6/1
N2 - 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.
AB - 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.
KW - C -algebras
KW - K-theory
KW - Unitary groups
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U2 - 10.1016/j.jfa.2012.03.016
DO - 10.1016/j.jfa.2012.03.016
M3 - Article
AN - SCOPUS:84859430200
SN - 0022-1236
VL - 262
SP - 4711
EP - 4730
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 11
ER -