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Volumn 1, Issue 2, 2008, Pages 259-304

The noncommutative geometry of k-graph C*-algebras

Author keywords

Graph algebra; index theorem; KK theory; spectral triple

Indexed keywords


EID: 85012459069     PISSN: 18652433     EISSN: 18655394     Source Type: Journal    
DOI: 10.1017/is007011015jkt013     Document Type: Article
Times cited : (36)

References (35)
  • 1
    • 0001348070 scopus 로고    scopus 로고
    • The C*-Algebras of Row-Finite Graphs
    • New York J. Math. BCPRSW (line 19 page 39)
    • T. Bates, D. Pask, I. Raeburn and W. Szymanski, The C*-Algebras of Row-Finite Graphs, New York J. Math. 6 (2000), 307-324. BCPRSW (line 19 page 39).
    • (2000) , vol.6 , pp. 307-324
    • Bates, T.1    Pask, D.2    Raeburn, I.3    Szymanski, W.4
  • 2
    • 84992266914 scopus 로고    scopus 로고
    • An Analytic Approach to Spectral Flow in von Neumann Algebras, in ‘Analysis
    • Geometry and Topology of Elliptic Operators-Papers in Honour of K. P. Wojciechowski’, World Scientific
    • M-T. Benemeur, A. Carey, J. Phillips, A. Rennie, F. Sukochev, K. Wojciechowski, An Analytic Approach to Spectral Flow in von Neumann Algebras, in ‘Analysis, Geometry and Topology of Elliptic Operators-Papers in Honour of K. P. Wojciechowski’, World Scientific, 2006, 297-352.
    • (2006) , pp. 297-352
    • Benemeur, M-T.1    Carey, A.2    Phillips, J.3    Rennie, A.4    Sukochev, F.5    Wojciechowski, K.6
  • 4
    • 3042759267 scopus 로고    scopus 로고
    • The Hochschild Class of the Chern Character of Semifinite Spectral Triples
    • A. Carey, J. Phillips, A. Rennie and F. Sukochev, The Hochschild Class of the Chern Character of Semifinite Spectral Triples, Journal of Functional Analysis 213 (2004), 111-153.
    • (2004) Journal of Functional Analysis , vol.213 , pp. 111-153
    • Carey, A.1    Phillips, J.2    Rennie, A.3    Sukochev, F.4
  • 5
    • 33748290318 scopus 로고    scopus 로고
    • The Local Index Theorem in Semifinite von Neumann Algebras I: Spectral Flow
    • A. Carey, J. Phillips, A. Rennie and F. Sukochev, The Local Index Theorem in Semifinite von Neumann Algebras I: Spectral Flow, Advances in Mathematics 202 (2006), 451-516.
    • (2006) Advances in Mathematics , vol.202 , pp. 451-516
    • Carey, A.1    Phillips, J.2    Rennie, A.3    Sukochev, F.4
  • 6
    • 33748184401 scopus 로고    scopus 로고
    • The Local Index Theorem in Semifinite von Neumann Algebras II: The Even Case
    • A. Carey, J. Phillips, A. Rennie and F. Sukochev, The Local Index Theorem in Semifinite von Neumann Algebras II: The Even Case, Advances in Mathematics 202 (2006) 517-554.
    • (2006) Advances in Mathematics , vol.202 , pp. 517-554
    • Carey, A.1    Phillips, J.2    Rennie, A.3    Sukochev, F.4
  • 7
    • 58449111199 scopus 로고    scopus 로고
    • The Chern Character of Semifinite Spectral Triples
    • math. OA/0611227
    • A. Carey, J. Phillips, A. Rennie, F. Sukochev The Chern Character of Semifinite Spectral Triples, math. OA/0611227.
    • Carey, A.1    Phillips, J.2    Rennie, A.3    Sukochev, F.4
  • 8
    • 0004261668 scopus 로고
    • Noncommutative Geometry
    • Academic Press
    • C. A. Connes, Noncommutative Geometry, Academic Press, 1994.
    • (1994)
    • Connes, C.A.1
  • 9
    • 0000151581 scopus 로고
    • The Local Index Formula in Noncommutative Geometry
    • GAFA
    • A. Connes and H. Moscovici, The Local Index Formula in Noncommutative Geometry, GAFA 5 (1995), 174-243.
    • (1995) , vol.5 , pp. 174-243
    • Connes, A.1    Moscovici, H.2
  • 10
    • 0003598756 scopus 로고
    • Von Neumann Algebras, North-Holland
    • D. J. Dixmier, Von Neumann Algebras, North-Holland, 1981.
    • (1981)
    • Dixmier, D.J.1
  • 11
    • 33644554667 scopus 로고    scopus 로고
    • On Higher-rank Graph C*-Algebras
    • Ph. D. Thesis, Univ. Wales
    • E. D. G. Evans, On Higher-rank Graph C*-Algebras, Ph. D. Thesis, Univ. Wales, 2002.
    • (2002)
    • Evans, E.D.G.1
  • 12
    • 84972546868 scopus 로고
    • Generalised s-numbers of -measurable operators
    • T. Fack and H. Kosaki, Generalised s-numbers of -measurable operators, Pacific J. Math. 123 (1986), 269-300.
    • (1986) Pacific J. Math. , vol.123 , pp. 269-300
    • Fack, T.1    Kosaki, H.2
  • 13
    • 0036344518 scopus 로고    scopus 로고
    • Product systems over right-angled Artin semigroups
    • N. J. Fowler and A. Sims, Product systems over right-angled Artin semigroups, Trans. Amer. Math. Soc. 354 (2002), 1487-1509.
    • (2002) Trans. Amer. Math. Soc. , vol.354 , pp. 1487-1509
    • Fowler, N.J.1    Sims, A.2
  • 15
    • 0003737316 scopus 로고    scopus 로고
    • Elements of Noncommutative Geometry
    • Birkhauser, Boston
    • J. M. Gracia-Bondia, J. C. Varilly and H. Figueroa, Elements of Noncommutative Geometry, Birkhauser, Boston, 2001.
    • (2001)
    • Gracia-Bondia, J.M.1    Varilly, J.C.2    Figueroa, H.3
  • 16
    • 85012436347 scopus 로고    scopus 로고
    • Analytic K-Homology, Oxford University Press
    • N. Higson and J. Roe, Analytic K-Homology, Oxford University Press, 2000.
    • (2000)
    • Higson, N.1    Roe, J.2
  • 17
    • 0035605444 scopus 로고    scopus 로고
    • Purely infinite and stable C*-algebras of graphs and dynamical systems
    • H. J. V. B. Hjelmborg, Purely infinite and stable C*-algebras of graphs and dynamical systems, Ergod. Th. & Dynam. Sys. 21 (2001), 1789-1808.
    • (2001) Ergod. Th. & Dynam. Sys. , vol.21 , pp. 1789-1808
    • Hjelmborg, H.J.V.B.1
  • 19
    • 0001241676 scopus 로고
    • The Operator K-Functor and Extensions of C*-Algebras, Math
    • USSR. Izv.
    • K. G. G. Kasparov, The Operator K-Functor and Extensions of C*-Algebras, Math. USSR. Izv. 16 (1981), 513-572.
    • (1981) , vol.16 , pp. 513-572
    • Kasparov, K.G.G.1
  • 21
    • 0000443450 scopus 로고    scopus 로고
    • Cuntz-Krieger Algebras of Directed Graphs
    • A. Kumjian, D. Pask and I. Raeburn, Cuntz-Krieger Algebras of Directed Graphs, Pacific J. Math. 184 (1998), 161-174.
    • (1998) Pacific J. Math. , vol.184 , pp. 161-174
    • Kumjian, A.1    Pask, D.2    Raeburn, I.3
  • 23
    • 85012562466 scopus 로고
    • Hilbert C*-Modules, Cambridge University Press, Cambridge
    • L. E. C. Lance, Hilbert C*-Modules, Cambridge University Press, Cambridge, 1995.
    • (1995)
    • Lance, L.E.C.1
  • 24
    • 0004071393 scopus 로고    scopus 로고
    • An Introduction to Noncommutative Spaces and their Geometries
    • New Series 51, Springer-Verlag, Berlin
    • G. Landi, An Introduction to Noncommutative Spaces and their Geometries, Lecture Notes in Physics, New Series 51, Springer-Verlag, Berlin, 1997.
    • (1997) Lecture Notes in Physics
    • Landi, G.1
  • 25
    • 0003598942 scopus 로고
    • Topological Algebras
    • Elsevier Science Publishers B. V.
    • M. A. Mallios, Topological Algebras, Selected Topics, Elsevier Science Publishers B. V., 1986.
    • (1986) Selected Topics
    • Mallios, M.A.1
  • 26
    • 0039014712 scopus 로고    scopus 로고
    • On the K-Theory of Cuntz-Krieger Algebras
    • Publ. Kyoto Univ.
    • D. Pask and I. Raeburn, On the K-Theory of Cuntz-Krieger Algebras, Publ. Kyoto Univ., 32 (1996), 415-443.
    • (1996) , vol.32 , pp. 415-443
    • Pask, D.1    Raeburn, I.2
  • 27
    • 33746769322 scopus 로고    scopus 로고
    • Rank-2 graphs whose C*-algebras are direct limits of circle algebras
    • D. Pask, I. Raeburn, M. Rørdam and A. Sims, Rank-2 graphs whose C*-algebras are direct limits of circle algebras, J. Funct. Anal. 239 (2006), 137-178.
    • (2006) J. Funct. Anal. , vol.239 , pp. 137-178
    • Pask, D.1    Raeburn, I.2    Rørdam, M.3    Sims, A.4
  • 28
    • 32544449019 scopus 로고    scopus 로고
    • The Noncommutative Geometry of Graph C*-Algebras I: The Index Theorem
    • D. Pask and A. Rennie, The Noncommutative Geometry of Graph C*-Algebras I: The Index Theorem, J. Funct. Anal. 233 (2006), 92-134.
    • (2006) J. Funct. Anal. , vol.233 , pp. 92-134
    • Pask, D.1    Rennie, A.2
  • 29
    • 0013195760 scopus 로고
    • An Index Theorem for Toeplitz Operators with Noncommutative Symbol Space
    • R. J. Phillips and I. Raeburn, An Index Theorem for Toeplitz Operators with Noncommutative Symbol Space, J. Funct. Anal. 120 (1994), 239-263.
    • (1994) J. Funct. Anal. , vol.120 , pp. 239-263
    • Phillips, R.J.1    Raeburn, I.2
  • 31
    • 0002499318 scopus 로고    scopus 로고
    • Morita Equivalence and Continuous-Trace C*-Algebras, Math. Surveys & Monographs
    • Providence
    • I. Raeburn and D. P. Williams, Morita Equivalence and Continuous-Trace C*-Algebras, Math. Surveys & Monographs, vol. 60, Amer. Math. Soc., Providence, 1998.
    • (1998) Amer. Math. Soc. , vol.60
    • Raeburn, I.1    Williams, D.P.2
  • 32
    • 0742306247 scopus 로고    scopus 로고
    • Cuntz-Krieger Algebras of Infinite Graphs and Matrices
    • I. Raeburn and W. Szymanski, Cuntz-Krieger Algebras of Infinite Graphs and Matrices, Trans. Amer. Math. Soc. 356, (2004), 39-59.
    • (2004) Trans. Amer. Math. Soc. , vol.356 , pp. 39-59
    • Raeburn, I.1    Szymanski, W.2
  • 33
    • 2442582407 scopus 로고    scopus 로고
    • Smoothness and Locality for Nonunital Spectral Triples
    • A. Rennie, Smoothness and Locality for Nonunital Spectral Triples, K-theory, 28 (2003), 127-165.
    • (2003) K-theory , vol.28 , pp. 127-165
    • Rennie, A.1
  • 34
    • 4043151597 scopus 로고    scopus 로고
    • Summability for Nonunital Spectral Triples
    • A. Rennie, Summability for Nonunital Spectral Triples, K-theory 31 (2004), 71-100.
    • (2004) K-theory , vol.31 , pp. 71-100
    • Rennie, A.1
  • 35
    • 0013536041 scopus 로고    scopus 로고
    • A Short Proof that Mn. A is local if A is Local and Fréchet
    • S. Larry B. Schweitzer, A Short Proof that Mn. A is local if A is Local and Fréchet, Int. J. math. 3.
    • Int. J. math. , vol.3
    • Larry, S.1    Schweitzer, B.2


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