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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
DOI: https://doi.org/10.1090/S0002-9939-08-09654-8
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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  • 1. A. Connes, Noncommutative Geometry, Academic Press, 1994. MR 1303779 (95j:46063)
  • 2. K. R. Davidson, C*-Algebras by Example, Fields Institute Monographs, vol. 6, Amer. Math. Soc., 1996. MR 1402012 (97i:46095)
  • 3. J. Glimm, On a certain class of operator algebras, Trans. Amer. Math. Soc. 95 (1960), 318-340. MR 0112057 (22:2915)
  • 4. E. Kirchberg, On subalgebras of the CAR-algebra, J. Functional Analysis 129, no. 1 (1995), 35-63. MR 1322641 (95m:46094b)
  • 5. E. Kirchberg, N. Phillips, Embedding of exact $ C^*$-algebras in the Cuntz algebra $ O_2$, J. Reine Angew. Math. 525 (2000), 17-53. MR 1780426 (2001d:46086a)
  • 6. S. A. Kruglyak, Coxeter functors for a certain class of $ \ast$-quivers, Ukrainian Math. J. 54(6) (2002), 967-978. MR 1956637 (2003k:16026)
  • 7. S. A. Kruglyak, V. I. Rabanovich, Yu. S. Samoilenko, On sums of projections, Funkt. Anal. i Prilozhen. 36, No. 3 (2002), 20-35. MR 1935900 (2004e:47021)
  • 8. S. Kruglyak, V. Rabanovich, Yu. Samoilenko, Decomposition of a scalar matrix into a sum of orthogonal projections, Linear Algebra and Its Appl. 370 (2003), 217-225. MR 1994329 (2004f:15045)
  • 9. S. A. Kruglyak, A. V. Royter, Locally scalar representations of graphs in the category of Hilbert spaces, Funkt. Anal. i Prilozhen. 39, No. 2 (2005), 13-30. MR 2161513 (2006g:16030)
  • 10. S. A. Kruglyak, Yu. S. Samoilenko, Unitary equivalence of sets of selfadjoint operators, Funkt. Anal. i Prilozhen. 14 (1980), no. 1, 60-62 (Russian). MR 565103 (81k:47031)
  • 11. S. A. Kruglyak, Yu. S. Samoilenko, On complexity of description of representations of $ \ast$-algebras generated by idempotents, Proc. Amer. Math. Soc. 128 (2000), 1655-1664. MR 1636978 (2000j:46099)
  • 12. T. Loring, Lifting Solutions to Perturbing Problems in C*-algebras, Fields Institute Monographs, vol. 8, Amer. Math. Soc., 1997. MR 1420863 (98a:46090)
  • 13. V. Ostrovskyi, Yu. Samoilenko, Introduction to the Theory of Representations of Finitely Presented *-Algebras, Reviews in Mathematics and Mathematical Physics, Vol. 11, Part 1, Harwood Academic Publishers, 1999. MR 1997101 (2005a:46123)
  • 14. V. I. Rabanovich, Yu. S. Samoilenko, When the sum of idempotents or projections is a multiple of unity, Funkt. Anal. i Prilozhen. 34, No. 4 (2000), 91-93. MR 1819651 (2001m:47004)
  • 15. S. Wassermann, Tensor products of free-group C*-algebras, Bull. London Math. Soc. 22 (1990), 375-380. MR 1058315 (91h:46103)

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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: https://doi.org/10.1090/S0002-9939-08-09654-8
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.

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