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You can see the arrows in a quiver operator algebra

Part of: Topological (rings and) algebras with an involution Linear spaces and algebras of operators

Published online by Cambridge University Press:  09 April 2009

Baruch Solel
Baruch Solel
Affiliation:
Department of Mathematics, Technion, Haifa 32000, Israel e-mail: mabaruch@technion.ac.il
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Abstract

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We prove that two quiver operator algebras can be isometrically isomorphic only if the quivers (=directed graphs) are isomorphic. We also show how the graph can be recovered from certain representations of the algebra.

Keywords

C*-correspondencetensor algebraquiverfree semigroup algebrafree semigroupoid algebrisomorphismdirected graph

MSC classification

Secondary: 47L55: Representations of (nonselfadjoint) operator algebras 47L75: Other nonselfadjoint operator algebras 46K50: Nonselfadjoint (sub)algebras in algebras with involution
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 77 , Issue 1 , August 2004 , pp. 111 - 122
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Arazy, J. and Solel, B., ‘Isometries of non-self-adjoint operator algebras’, J. Funct. Anal. 90 (1990), 284–305.CrossRefGoogle Scholar
[2]Arveson, W. B., ‘Operator algebras and measure preserving automorphisms’, Acta Math. 118 (1967), 95–109.CrossRefGoogle Scholar
[3]Baillet, M., Denizeau, Y. and Havet, J.-F., ‘Indice d'une esperance conditionnelle’, Comp. Math. 66 (1988), 199–236.Google Scholar
[4]Brenken, B., ‘C*-algebras of infinite graphs and Cuntz-Krieger algebras’, Canad. Math. Bull. 45 (2002), 321–336.CrossRefGoogle Scholar
[5]Cuntz, J. and Krieger, W., ‘A class of C*-algebras and topological Markov chains’, Invent. Math. 56 (1980), 251–268.CrossRefGoogle Scholar
[6]Davidson, K. R. and Pitts, D. R., ‘The algebraic structure of noncommutative analytic Toeplitz algebras’, Math. Ann. 311 (1998), 275–303.CrossRefGoogle Scholar
[7]Exel, R. and Laca, M., ‘Cuntz-Krieger algebras for infinite matrices’, J. Reine Angew. Math 512 (1999), 119–172.CrossRefGoogle Scholar
[8]Kribs, D. W. and Power, S. C., ‘Free semigroupoid algebras’, preprint.Google Scholar
[9]Kumjian, A., Pask, D. and Raeburn, I., ‘Cuntz-Krieger algebras of directed graphs’, Pacific J. Math. 184 (1998), 161–174.CrossRefGoogle Scholar
[10]Lance, E. C., Hilbert C*-modules—a toolkit for operator algebraists, London Math. Soc. Lecture Notes (Cambridge Univ. Press, Cambridge, UK, 1995).CrossRefGoogle Scholar
[11]Muhly, P. S. and Solel, B., ‘The curvature and index of completely positive maps’, Proc. London Math. Soc. (3) 87 (2003), 748–778.CrossRefGoogle Scholar
[12]Muhly, P. S. and Solel, B., ‘Tensor algebras over C*-correspondences (representations, dilations and C*-envelopes)’, J. Funct. Anal. 158 (1998), 389–457.CrossRefGoogle Scholar
[13]Laca, M., Fowler, N. and Raeburn, I., ‘The C*-algebras of infinite graphs’, Proc. Amer. Math. Soc. 128 (2000), 2319–2327.Google Scholar
[14]Popescu, G., ‘von Neumann inequality for (B(ℋ))1’, Math. Scand. 68 (1991), 292–304.CrossRefGoogle Scholar
[15]Popescu, G., ‘Non commutative disc algebras and their representations’, Proc. Amer. Math. Soc. 124 (1996), 2137–2148.CrossRefGoogle Scholar