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C*-Algebras of Infinite Real Rank

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
A. "Alex" Chigogidze, Professor and Department Chair (Creator)
Institution
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/

Abstract: We introduce the notion of weakly (strongly) infinite real rank for unital C *-algebras. It is shown that a compact space X is weakly (strongly) infine-dimensional if and only if C(X) has weakly (strongly) infinite real rank. Some other properties of this concept are also investigated. In particular, we show that the group C *-algebra C * (F1) of the free group on countable number of generators has strongly infinite real rank.

Additional Information

Publication
arXiv:math/0205142v1 [math.GN] 14 May 2002
Language: English
Date: 2002
Keywords
Real rank, Bounded rank, Weakly infinite-dimensional compacta