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bibliography for operator algebras in mathematical physics and AQFT-A to K (Topic)

0.1 Bibliography for Operator Algebras in Mathematical Physics and Algebraic Quantum Field Theories (AQFT):

Alphabetical order: letters from A to K

References

[1]   Akutsu, Y. and Wadati, M. (1987). Knot invariants and critical statistical systems. Journal of the Physics Society of Japan, 56, 839–842.

[2]   Alexander, J. W. (1930). The combinatorial theory of complexes. Annals of Mathematics, (2) 31, 294–322.

[3]   Andrews, G. E., Baxter, R. J. and Forrester, P.J. (1984). Eight vertex SOS model and generalized Rogers–Ramanujan type identities. Journal of Statistical Physics, 35, 193–266.

[4]   Aoi, H. and Yamanouchi, T. (in press). Construction of a canonical subfactor for an inclusion of factors with a common Cartan subalgebra. Hokkaido Mathematical Journal.

[5]   Arcuri, R. C., Gomes, J. F. and D. I. Olive (1987). Conformal subalgebras and symmetric spaces. Nuclear Physics B, 285, 327–339.

[6]   Artin, E. (1947). Theory of braids. Annals of Mathematics, 48 101–126.

[7]   Asaeda, M. (2007). Galois groups and an obstruction to principal graphs of subfactors. International Journal of Mathematics, 18, 191–202. math.OA/0605318.

[8]   Asaeda, M. and Haagerup, U. (1999). Exotic subfactors of finite depth with Jones indices (5 + √ ---
  13)2 and (5 + √ ---
  17)2. Communications in Mathematical Physics, 202, 1–63.

[9]   Asaeda, M. and Yasuda, S. (preprint 2007). On Haagerup’s list of potential principal graphs of subfactors. arXiv:0711.4144.

[10]   Atiyah, M. (1967). K-theory. W. A. Benjamin Inc., New York.

[11]   Atiyah, M. (1989). Topological quantum field theory. Publication Mathématiques IHES, 68, 175–186.

[12]   Aubert, P.-L. (1976). Théorie de Galois pour une W-algèbre. Commentarii Mathematici Helvetici, 39 (51), 411–433.

[13]   Baez, J. C., Segal, I. E. and Zhou, Z. (1992). Introduction to algebraic and constructive quantum field theory. Princeton University Press.

[14]   Bakalov, B. and Kirillov, A. Jr. (2001). Lectures on tensor categories and modular functors. University Lecture Series 21, Amer. Math. Soc.

[15]   Banica, T. (1997). Le groupe quantique compact libre U(n), Communications in Mathematical Physics, 190, 143–172.

[16]   Banica, T. (1998). Hopf algebras and subfactors associated to vertex models. Journal of Functional Analysis, 159, 243–266.

[17]   Banica, T. (1999). Representations of compact quantum groups and subfactors. Journal für die Reine und Angewandte Mathematik, 509, 167–198.

[18]   Banica, T. (1999). Fusion rules for representations of compact quantum groups. Expositiones Mathematicae, 17, 313–337.

[19]   Banica, T. (1999). Symmetries of a generic coaction. Mathematische Annalen, 314, 763–780.

[20]   Banica, T. (2000). Compact Kac algebras and commuting squares. Journal of Functional Analysis, 176, 80–99.

[21]   Banica, T. (2001). Subfactors associated to compact Kac algebras. Integral Equations Operator Theory, 39, 1–14.

[22]   Banica, T. (2002). Quantum groups and Fuss-Catalan algebras. Communications in Mathematical Physics, 226, 221–232

[23]   Banica, T. (2005). The planar algebra of a coaction. Journal of Operator Theory 53, 119–158.

[24]   Banica, T. (2005). Quantum automorphism groups of homogeneous graphs. Journal of Functional Analysis, 224, 243–280.

[25]   Banica, T. (2005). Quantum automorphism groups of small metric spaces. Pacific Journal of Mathematics, 219, 27–51.

[26]   Baxter, R. J. (1981).Rogers–Ramanujan identities in the Hard Hexagon model. Journal of Statistical Physics, 26, 427–452.

[27]   Baxter, R. J. (1982). Exactly solved models in statistical mechanics. Academic Press, New York.

[28]   Baxter, R. J. (1988). The superintegrable chiral Potts model. Physics Letters A, 133, 185–189.

[29]   Baxter, R. J. (1989). A simple solvable Z4(N) Hamiltonian. Physics Letters A, 140, 155–157.

[30]   Baxter, R. J. (1989). Superintegrable Chiral Potts model: thermodynamic properties, an “inverse” model, and a simple associated Hamiltonian. Journal of Statistical Physics, 57, 1–39.

[31]   Baxter, R. J., Kelland, S. B. and Wu, F. Y. (1976). Potts model or Whitney Polynomial. Journal of Physics. A. Mathematical and General, 9, 397–406.

[32]   Baxter, R. J., Perk, J. H. H. and Au-Yang, H. (1988). New solutions of the star-triangle relations for the chiral Potts model. Physics Letters A 128, 138–142.

[33]   Baxter, R. J., Temperley, H. N. V. and Ashley, S. E. (1978). Triangular Potts model and its transition temperature and related models. Proceedings of the Royal Society of London A, 358, 535–559.

[34]   Behrend, R. E., Evans, D. E. (preprint 2003). Integrable Lattice Models for Conjugate An(1). hep-th/0309068.

[35]   Behrend, R. E., Pearce, P. A., Petkova, V. B. and Zuber, J-B. (2000). Boundary conditions in rational conformal field theories. Nuclear Physics B, 579, 707–773.

[36]   Belavin, A. A., Polyakov, A. M. and Zamolodchikov, A. B. (1980). Infinite conformal symmetry in two-dimensional quantum field theory. Nuclear Physics B, 241, 333–380.

[37]   Berezin, F. A. (1966). A method of second quantization. Academic Press, London/New York.

[38]   Bertozzini, P., Conti, R. and Longo, R. (1998) Covariant sectors with infinite dimension and positivity of the energy. Communications in Mathematical Physics, 193, 471–492.

[39]   Bion-Nadal, J. (1992). Subfactor of the hyperfinite II1 factor with Coxeter graph E6 as invariant. Journal of Operator Theory, 28, 27–50.

[40]   Birman, J. (1974). Braids, links and mapping class groups. Annals of Mathematical Studies, 82.

[41]   Birman, J. S. and Wenzl, H. (1989). Braids, link polynomials and a new algebra. Transactions of the American Mathematical Society, 313, 249–273.

[42]   Bisch, D. (1990). On the existence of central sequences in subfactors. Transactions of the American Mathematical Society, 321, 117–128.

[43]   Bisch, D. (1992). Entropy of groups and subfactors. Journal of Functional Analysis, 103, 190–208.

[44]   Bisch, D. (1994). A note on intermediate subfactors. Pacific Journal of Mathematics, 163, 201–216.

[45]   Bisch, D. (1994). On the structure of finite depth subfactors. in Algebraic methods in operator theory, (ed. R. Curto and P. E. T. Jörgensen), Birkhäuser, 175–194.

[46]   Bisch, D. (1994). Central sequences in subfactors II. Proceedings of the American Mathematical Society, 121, 725–731.

[47]   Bisch, D. (1994). An example of an irreducible subfactor of the hyperfinite II1 factor with rational, non-integer index. Journal für die Reine und Angewandte Mathematik, 455, 21–34.

[48]   Bisch, D. (1997). Bimodules, higher relative commutants and the fusion algebra associated to a subfactor. In Operator algebras and their applications. Fields Institute Communications, Vol. 13, American Math. Soc., 13–63.

[49]   Bisch, D. (1998). Principal graphs of subfactors with small Jones index. Mathematische Annalen, 311, 223–231.

[50]   Bisch, D. (2002). Subfactors and planar algebras. Proc. ICM-2002, Beijing, 2, 775–786.

[51]   Bisch, D. and Haagerup, U. (1996). Composition of subfactors: New examples of infinite depth subfactors. Annales Scientifiques de l’École Normale Superieur, 29, 329–383.

[52]   Bisch, D. and Jones, V. F. R. (1997). Algebras associated to intermediate subfactors. Inventiones Mathematicae, 128, 89–157.

[53]   Bisch, D. and Jones, V. F. R. (1997). A note on free composition of subfactors. In Geometry and Physics, (Aarhus 1995), Marcel Dekker, Lecture Notes in Pure and Applied Mathematics, Vol. 184, 339–361.

[54]   Bisch, D. and Jones, V. F. R. (2000). Singly generated planar algebras of small dimension. Duke Mathematical Journal, 101, 41–75.

[55]   Bisch, D. and Jones, V. F. R. (2003). Singly generated planar algebras of small dimension. II Advances in Mathematics, 175, 297–318.

[56]   Bisch, D., Nicoara, R. and Popa, S. (2007). Continuous families of hyperfinite subfactors with the same standard invariant. International Journal of Mathematics, 18, 255–267. math.OA/0604460.

[57]   Bisch, D. and Popa, S. (1999). Examples of subfactors with property T standard invariant. Geometric and Functional Analysis, 9, 215–225.

[58]   Böckenhauer, J. (1996). An algebraic formulation of level one Wess-Zumino-Witten models. Reviews in Mathematical Physics, 8, 925–947.

[59]   Böckenhauer, J. and Evans, D. E. (1998). Modular invariants, graphs and α-induction for nets of subfactors I. Communications in Mathematical Physics, 197, 361–386.

[60]   Böckenhauer, J. and Evans, D. E. (1999). Modular invariants, graphs and α-induction for nets of subfactors II. Communications in Mathematical Physics, 200, 57–103.

[61]   Böckenhauer, J. and Evans, D. E. (1999). Modular invariants, graphs and α-induction for nets of subfactors III. Communications in Mathematical Physics, 205, 183–228.

[62]   Böckenhauer, J. and Evans, D. E. (2000). Modular invariants from subfactors: Type I coupling matrices and intermediate subfactors. Communications in Mathematical Physics, 213, 267–289.

[63]   Böckenhauer, J. and Evans, D. E. (2002). Modular invariants from subfactors. in Quantum Symmetries in Theoretical Physics and Mathematics (ed. R. Coquereaux et al.), Comtemp. Math. 294, Amer. Math. Soc., 95–131. math.OA/0006114.

[64]   Böckenhauer, J. and Evans, D. E. (2001). Modular invariants and subfactors. in Mathematical Physics in Mathematics and Physics (ed. R. Longo), The Fields Institute Communications 30, Providence, Rhode Island: AMS Publications, 11–37. math.OA/0008056.

[65]   Böckenhauer, J., Evans, D. E. and Kawahigashi, Y. (1999). On α-induction, chiral generators and modular invariants for subfactors. Communications in Mathematical Physics, 208, 429–487. math.OA/9904109.

[66]   Böckenhauer, J., Evans, D. E. and Kawahigashi, Y. (2000). Chiral structure of modular invariants for subfactors. Communications in Mathematical Physics, 210, 733–784. math.OA/9907149.

[67]   Böckenhauer, J., Evans, D. E. and Kawahigashi, Y. (2001). Longo-Rehren subfactors arising from α-induction. Publications of the RIMS, Kyoto University, 37, 1–35. math.OA/0002154.

[68]   de Boer, J. and Goeree, J. (1991). Markov traces and II1 factors in conformal field theory. Communications in Mathematical Physics, 139, 267–304.

[69]   Bongaarts, P. J. M. (1970). The electron-positron field, coupled to external electromagnetic potentials as an elementary C-algebra theory. Annals of Physics, 56, 108–138.

[70]   Bratteli, O. (1972). Inductive limits of finite dimensional C-algebras. Transactions of the American Mathematical Society, 171, 195–234.

[71]   Brunetti, R., Guido, D. and Longo, R. (1993). Modular structure and duality in conformal quantum field theory. Communications in Mathematical Physics, 156, 201–219.

[72]   Brunetti, R., Guido, D. and Longo, R. (1995). Group cohomology, modular theory and space-time symmetries. Reviews in Mathematical Physics, 7 57–71.

[73]   Buchholz, D., Doplicher, S., Longo, R. and Roberts, J. E. (1993). Extensions of automorphisms and gauge symmetries. Communications in Mathematical Physics, 155, 123–134.

[74]   Buchholz, D., Mack, G. and Todorov, I. (1988). The current algebra on the circle as a germ of local field theories. Nuclear Physics B (Proc. Suppl.), B5, 20–56.

[75]   Buchholz, D. and Schulz-Mirbach, H. (1990). Haag duality in conformal quantum field theoery, Reviews in Mathematical Physics, 2 105–125.

[76]   Camp, W., and Nicoara, R. (preprint 2007). Subfactors and Hadamard matrices. arXiv:0704.1128.

[77]   Cappelli, A., Itzykson, C. and Zuber, J.-B. (1987). The A-D-E classification of minimal and A1(1) conformal invariant theories. Communications in Mathematical Physics, 113, 1–26.

[78]   Carpi, S. (1998). Absence of subsystems for the Haag-Kastler net generated by the energy-momentum tensor in two-dimensional conformal field theory. Letters in Mathematical Physics, 45, 259–267.

[79]   Carpi, S. (2003). The Virasoro algebra and sectors with infinite statistical dimension. Annales Henri Poincaré, 4, 601–611. math.OA/0203027.

[80]   Carpi, S. (2004). On the representation theory of Virasoro nets. Communications in Mathematical Physics, 244, 261–284. math.OA/0306425.

[81]   Carpi, S. (2005). Intersecting Jones projections. International Journal of Mathematics, 16, 687–691. math.OA/0412457.

[82]   Carpi, S. and Conti, R. (2001). Classification of subsystems for local nets with trivial superselection structure. Communications in Mathematical Physics, 217, 89–106.

[83]   Carpi, S. and Conti, R. (2005). Classification of subsystems for graded-local nets with trivial superselection structure. Communications in Mathematical Physics. 253, 423–449. math.OA/0312033.

[84]   Carpi, S., Kawahigashi, Y. and Longo, R. (in press). Structure and classification of superconformal nets. Annales Henri Poincaré. arXiv:0705.3609.

[85]   Carpi, S. and Weiner, M. (2005). On the uniqueness of diffeomorphism symmetry in Conformal Field Theory. Communications in Mathematical Physics, 258, 203–221. math.OA/0407190.

[86]   Ceccherini, T. (1996). Approximately inner and centrally free commuting squares of type II1 factors and their classification. Journal of Functioanl Analysis, 142, 296–336.

[87]   Chen, J. (1993). The Connes invariant χ(M) and cohomology of groups. Ph. D. dissertation at University of California, Berkeley.

[88]   Choda, M. (1989). Index for factors generated by Jones’ two sided sequence of projections. Pacific Journal of Mathematics, 139, 1–16.

[89]   Choda, M. (1991). Entropy for -endomorphisms and relative entropy for subalgebras. Journal of Operator Theory, 25, 125–140.

[90]   Choda, M. (1992). Entropy for canonical shift. Transactions of the American Mathematical Society, 334, 827–849.

[91]   Choda, M. (1993). Duality for finite bipartite graphs (with applications to II1 factors). Pacific Journal of Mathematics, 158, 49–65.

[92]   Choda, M. (1994). Square roots of the canonical shifts. Journal of Operator Theory, 31, 145–163.

[93]   Choda, M. (1994). Extension algebras via -endomorphisms. in Subfactors — Proceedings of the Taniguchi Symposium, Katata —, (ed. H. Araki, et al.), World Scientific, 105–128.

[94]   Choda, M. and Hiai, F. (1991). Entropy for canonical shifts. II. Publications of the RIMS, Kyoto University, 27, 461–489.

[95]   Choda, M. and Kosaki, H. (1994). Strongly outer actions for an inclusion of factors. Journal of Functional Analysis, 122, 315–332.

[96]   Christensen, E. (1979). Subalgebras of a finite algebra. Mathematische Annalen, 243, 17–29.

[97]   Combes, F. (1968). Poids sur une C-algèbre. Journal de Mathématiques Pures et Appliquées, 47, 57–100.

[98]   Connes, A. (1973). Une classification des facteurs de type III. Annales Scientifiques de l’École Normale Supérieure, 6, 133–252.

[99]   Connes, A. (1975). Outer conjugacy classes of automorphisms of factors. Annales Scientifiques de l’École Normale Supérieure, 8, 383–419.

[100]   Connes, A. (1975). Hyperfinite factors of type III-0 and Krieger’s factors. Journal of Functional Analysis, 18, 318–327.

[101]   Connes, A. (1975). Sur la classification des facteurs de type II. Comptes Rendus de l’Academie des Sciences, Série I, Mathématiques, 281, 13–15.

[102]   Connes, A. (1975). A factor not antiisomorphic to itself. Annals of Mathematics, 101, 536–554.

[103]   Connes, A. (1976). Classification of injective factors. Annals of Mathematics, 104, 73–115.

[104]   Connes, A. (1976). Outer conjugacy of automorphisms of factors. Symposia Mathematica, XX, 149–160.

[105]   Connes, A. (1976). On the classification of von Neumann algebras and their automorphisms. Symposia Mathematica, XX, 435–478.

[106]   Connes, A. (1977). Periodic automorphisms of the hyperfinite factor of type II1. Acta Scientiarum Mathematicarum, 39, 39–66.

[107]   Connes, A. (1978). On the cohomology of operator algebras. Journal of Functional Analysis, 28, 248–253.

[108]   Connes, A. (1979). Sur la théorie non commutative de l’integration. Springer Lecture Notes in Math., 725, 19–143.

[109]   Connes, A. (1980). C-algebres et geomètrie différentielle. Comptes Rendus de l’Academie des Sciences, Série I, Mathématiques, 559–604.

[110]   Connes, A. (1980). Spatial theory of von Neumann algebras. Journal of Functional Analysis, 35 (1980), 153–164.

[111]   Connes, A. (1981). An analogue of the Thom isomorphism for crossed products of a C-algebra by an action of R. Advances in Mathematics, 39, 311–355.

[112]   Connes, A. (1982). Foliations and Operator Algebras. Proceedings of Symposia in Pure Mathematics. ed. R. V. Kadison, 38, 521–628.

[113]   Connes, A. (1982). Classification des facteurs. Proceedings of the Symposia in Pure Mathematics (II), 38, 43–109.

[114]   Connes, A. (1985). Non-commutative differential geometry I–II. Publication Mathématiques IHES, 62, 41–144.

[115]   Connes, A. (1985). Factors of type III-1, property Lλ and closure of inner automorphisms. Journal of Operator Theory, 14, 189–211.

[116]   Connes, A. (1985). Non Commutative Differential Geometry, Chapter II: De Rham homology and non commutative algebra. Publication Mathématiques IHES, 62, 257–360.

[117]   Connes, A. (1994). Noncommutative geometry. Academic Press.

[118]   Connes, A. and Evans, D. E. (1989). Embeddings of U(1)-current algebras in non-commutative algebras of classical statistical mechanics. Communications in Mathematical Physics, 121, 507–525.

[119]   Connes, A. and Higson, N. (1990). Déformations, morphismes asymptotiques et K-théorie bivariante. Comptes Rendus de l’ Academie des Sciences, Série I, Mathématiques, 311, 101–106.

[120]   Connes, A. and Karoubi, M. (1988). Caractere multiplicatif d’un module de Fredholm. K-theory, 2 431–463.

[121]   Connes, A. and Krieger, W. (1977). Measure space automorphism groups, the normalizer of their full groups, and approximate finiteness. Journal of Functional Analysis, 24, 336–352.

[122]   Connes, A. and Rieffel, M. (1985). Yang-Mills for non-commutative tori. Contemporary Mathematics, 62, 237–265.

[123]   Connes, A. and Skandalis, G. (1984). The longitudinal index theorem for foliations. Publications of the RIMS, Kyoto University, 20, 1139–1183.

[124]   Connes, A. and Störmer, E. (1975). Entropy for automorphisms of II1 von Neumann algebras. Acta Mathematica, 134, 289–306.

[125]   Connes, A. and Takesaki, M. (1977). The flow of weights on factors of type III. Tohoku Mathematical Journal, 29, 73–555.

[126]   Conti, R., Doplicher, S., and Roberts, J. E. (2001). Superselection theory for subsystems. Communications in Mathematical Physics, 218, 263–281.

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[128]   Coquereaux, R. (2005) The A2 Ocneanu quantum groupoid. in Algebraic structures and their representations, Contemporary Mathematics, 376, 227–247. hep-th/0311151.

[129]   Coquereaux, R. and Schieber, G. (2002). Twisted partition functions for ADE boundary conformal field theories and Ocneanu algebras of quantum symmetries. Journal of Geometry and Physics, 42, 216–258.

[130]   Coquereaux, R. and Schieber, G. (2003). Determination of quantum symmetries for higher ADE systems from the modular T matrix. Journal of Mathematical Physics, 44, 3809–3837. hep-th/0203242.

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