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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On universal $ C^*$-algebras generated by $ n$ projections with scalar sum


Author: Tatiana Shulman
Journal: Proc. Amer. Math. Soc. 137 (2009), 115-122
MSC (2000): Primary 46L05; Secondary 46L35
Published electronically: August 14, 2008
MathSciNet review: 2439432
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Abstract: We study the universal $ C^*$-algebras generated by $ n$ projections $ p_1,\dotsc,p_n$ subject to the relation $ p_1+\cdots +p_n=\lambda 1$, $ \lambda\in\mathbb{R}$. The questions of when these $ C^*$-algebras are type I, nuclear or exact are considered. It is proved also that among these $ C^*$-algebras there is a continuum of mutually nonisomorphic ones.


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Additional Information

Tatiana Shulman
Affiliation: Department of Mathematics, University of New Hampshire, Durham, New Hampshire 03824
Email: tatiana_shulman@yahoo.com

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09654-8
PII: S 0002-9939(08)09654-8
Keywords: Projection, universal $C^*$-algebra of a relation, tracial state, nuclear and exact $C^*$-algebras
Received by editor(s): July 19, 2007
Published electronically: August 14, 2008
Communicated by: Marius Junge
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.