# PlanetPhysics/Bibliography for Observable Operator Algebras
## Topical References for Operator Algebras in Theoretical Physics and Algebraic Quantum Field Theories (AQFT):

\begin{thebibliography} {299}
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* ↑ Akutsu, Y. and Wadati, M. (1987). Knot invariants and critical statistical systems. Journal of the Physics Society of Japan , {\mathbf 56}, 839--842.
* ↑ Alexander, J. W. (1930). The combinatorial theory of complexes. Annals of Mathematics , {\mathbf (2) 31}, 294--322.
* ↑ 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 , {\mathbf 35}, 193--266.
* ↑ Aoi, H. and Yamanouchi, T. (in press). Construction of a canonical subfactor for an inclusion of factors with a common Cartan subalgebra. {\rm Hokkaido Mathematical Journal}.
* ↑ Arcuri, R. C., Gomes, J. F. and D. I. Olive (1987). Conformal subalgebras and symmetric spaces. Nuclear Physics B , {\mathbf 285}, 327--339.
* ↑ Artin, E. (1947). Theory of braids. Annals of Mathematics , {\mathbf 48} 101--126.
* ↑ Asaeda, M. (2007). Galois groups and an obstruction to principal graphs of subfactors. International Journal of Mathematics , {\mathbf 18}, 191--202. math.OA/0605318.
* ↑ Asaeda, M. and Haagerup, U. (1999). Exotic subfactors of finite depth with Jones indices ${(5+{\sqrt {13}})}/{2}$ and ${(5+{\sqrt {17}})}/{2}$. Communications in Mathematical Physics , {\mathbf 202}, 1--63.
* ↑ Asaeda, M. and Yasuda, S. (preprint 2007). On Haagerup's list of potential principal graphs of subfactors. arXiv:0711.4144.
* ↑ Atiyah, M. (1967). $K$-theory. W. A. Benjamin Inc., New York .
* ↑ Atiyah, M. (1989). Topological quantum field theory. Publication Math\'ematiques IHES , {\mathbf 68}, 175--186.
* ↑ Aubert, P.-L. (1976). Th\'eorie de Galois pour une $W^{*}$-alg\`ebre. Commentarii Mathematici Helvetici , {\mathbf 39 (51)}, 411--433.
* ↑ Baez, J. C., Segal, I. E. and Zhou, Z. (1992). Introduction to algebraic and constructive quantum field theory. Princeton University Press .
* ↑ Bakalov, B. and Kirillov, A. Jr. (2001). Lectures on tensor categories and modular functors. University Lecture Series {\mathbf 21}, Amer. Math. Soc.
* ↑ Banica, T. (1997). Le groupe quantique compact libre $U(n)$, Communications in Mathematical Physics , {\mathbf 190}, 143--172.
* ↑ Banica, T. (1998). Hopf algebras and subfactors associated to vertex models. Journal of Functional Analysis , {\mathbf 159}, 243--266.
* ↑ Banica, T. (1999). Representations of compact quantum groups and subfactors. Journal f\"ur die Reine und Angewandte Mathematik , {\mathbf 509}, 167--198.
* ↑ Banica, T. (1999). Fusion rules for representations of compact quantum groups. Expositiones Mathematicae , {\mathbf 17}, 313--337.
* ↑ Banica, T. (1999). Symmetries of a generic coaction. Mathematische Annalen , {\mathbf 314}, 763--780.
* ↑ Banica, T. (2000). Compact Kac algebras and commuting squares. Journal of Functional Analysis , {\mathbf 176}, 80--99.
* ↑ Banica, T. (2001). Subfactors associated to compact Kac algebras. Integral Equations Operator Theory , {\mathbf 39}, 1--14.
* ↑ Banica, T. (2002). Quantum groups and Fuss-Catalan algebras. Communications in Mathematical Physics , {\mathbf 226}, 221--232
* ↑ Banica, T. (2005). The planar algebra of a coaction. Journal of Operator Theory {\mathbf 53}, 119--158.
* ↑ Banica, T. (2005). Quantum automorphism groups of homogeneous graphs. Journal of Functional Analysis , {\mathbf 224}, 243--280.
* ↑ Banica, T. (2005). Quantum automorphism groups of small metric spaces. Pacific Journal of Mathematics , {\mathbf 219}, 27--51.
* ↑ Baxter, R. J. (1981).Rogers--Ramanujan identities in the Hard Hexagon model. Journal of Statistical Physics , {\mathbf 26}, 427--452.
* ↑ Baxter, R. J. (1982). Exactly solved models in statistical mechanics . Academic Press, New York.
* ↑ Baxter, R. J. (1988). The superintegrable chiral Potts model. Physics Letters A , {\mathbf 133}, 185--189.
* ↑ Baxter, R. J. (1989). A simple solvable $Z_{4}(N)$ Hamiltonian. Physics Letters A , {\mathbf 140}, 155--157.
* ↑ Baxter, R. J. (1989). Superintegrable Chiral Potts model: thermodynamic properties, an "inverse" model, and a simple associated Hamiltonian. {\em Journal of Statistical Physics}, {\mathbf 57}, 1--39.
* ↑ Baxter, R. J., Kelland, S. B. and Wu, F. Y. (1976). Potts model or Whitney Polynomial. Journal of Physics. A. Mathematical and General , {\mathbf 9}, 397--406.
* ↑ 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 {\mathbf 128}, 138--142.
* ↑ 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 , {\mathbf 358}, 535--559.
* ↑ Behrend, R. E., Evans, D. E. (preprint 2003). Integrable Lattice Models for Conjugate $A_{n}^{(1)}$. hep-th/0309068.
* ↑ Behrend, R. E., Pearce, P. A., Petkova, V. B. and Zuber, J-B. (2000). Boundary conditions in rational conformal field theories. Nuclear Physics B , {\mathbf 579}, 707--773.
* ↑ Belavin, A. A., Polyakov, A. M. and Zamolodchikov, A. B. (1980). Infinite conformal symmetry in two-dimensional quantum field theory. Nuclear Physics B , {\mathbf 241}, 333--380.
* ↑ Berezin, F. A. (1966). A method of second quantization. Academic Press , London/New York.
* ↑ Bertozzini, P., Conti, R. and Longo, R. (1998) Covariant sectors with infinite dimension and positivity of the energy. Communications in Mathematical Physics , {\mathbf 193}, 471--492.
* ↑ Bion-Nadal, J. (1992). Subfactor of the hyperfinite $II_{1}$ factor with Coxeter graph $E_{6}$ as invariant. Journal of Operator Theory , {\mathbf 28}, 27--50.
* ↑ Birman, J. (1974). Braids, links and mapping class groups. Annals of Mathematical Studies , {\mathbf 82}.
* ↑ Birman, J. S. and Wenzl, H. (1989). Braids, link polynomials and a new algebra. Transactions of the American Mathematical Society , {\mathbf 313}, 249--273.
* ↑ Bisch, D. (1990). On the existence of central sequences in subfactors. Transactions of the American Mathematical Society , {\mathbf 321}, 117--128.
* ↑ Bisch, D. (1992). Entropy of groups and subfactors. Journal of Functional Analysis , {\mathbf 103}, 190--208.
* ↑ Bisch, D. (1994). A note on intermediate subfactors. Pacific Journal of Mathematics , {\mathbf 163}, 201--216.
* ↑ Bisch, D. (1994). On the structure of finite depth subfactors. in Algebraic methods in operator theory , (ed. R. Curto and P. E. T. J\"orgensen), Birkh\"auser, 175--194.
* ↑ Bisch, D. (1994). Central sequences in subfactors II. Proceedings of the American Mathematical Society , {\mathbf 121}, 725--731.
* ↑ Bisch, D. (1994). An example of an irreducible subfactor of the hyperfinite II$_{1}$ factor with rational, non-integer index. {\em Journal f\"ur die Reine und Angewandte Mathematik}, {\mathbf 455}, 21--34.
* ↑ 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.
* ↑ Bisch, D. (1998). Principal graphs of subfactors with small Jones index. Mathematische Annalen , {\mathbf 311}, 223--231.
* ↑ Bisch, D. (2002). Subfactors and planar algebras. Proc. ICM-2002, Beijing , {\mathbf 2}, 775--786.
* ↑ Bisch, D. and Haagerup, U. (1996). Composition of subfactors: New examples of infinite depth subfactors. {\em Annales Scientifiques de l'\'Ecole Normale Superieur}, {\mathbf 29}, 329--383.
* ↑ Bisch, D. and Jones, V. F. R. (1997). Algebras associated to intermediate subfactors. Inventiones Mathematicae , {\mathbf 128}, 89--157.
* ↑ 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.
* ↑ Bisch, D. and Jones, V. F. R. (2000). Singly generated planar algebras of small dimension. Duke Mathematical Journal , {\mathbf 101}, 41--75.
* ↑ Bisch, D. and Jones, V. F. R. (2003). Singly generated planar algebras of small dimension. II Advances in Mathematics , {\mathbf 175}, 297--318.
* ↑ Bisch, D., Nicoara, R. and Popa, S. (2007). Continuous families of hyperfinite subfactors with the same standard invariant. International Journal of Mathematics , {\mathbf 18}, 255--267. math.OA/0604460.
* ↑ Bisch, D. and Popa, S. (1999). Examples of subfactors with property T standard invariant. Geometric and Functional Analysis , {\mathbf 9}, 215--225.
* ↑ B\"ockenhauer, J. (1996). An algebraic formulation of level one Wess-Zumino-Witten models. Reviews in Mathematical Physics , {\mathbf 8}, 925--947.
* ↑ B\"ockenhauer, J. and Evans, D. E. (1998). Modular invariants, graphs and $\alpha$-induction for nets of subfactors I. Communications in Mathematical Physics , {\mathbf 197}, 361--386.
* ↑ B\"ockenhauer, J. and Evans, D. E. (1999). Modular invariants, graphs and $\alpha$-induction for nets of subfactors II. Communications in Mathematical Physics , {\mathbf 200}, 57--103.
* ↑ B\"ockenhauer, J. and Evans, D. E. (1999). Modular invariants, graphs and $\alpha$-induction for nets of subfactors III. Communications in Mathematical Physics , {\mathbf 205}, 183--228.
* ↑ B\"ockenhauer, J. and Evans, D. E. (2000). Modular invariants from subfactors: Type I coupling matrices and intermediate subfactors. Communications in Mathematical Physics , {\mathbf 213}, 267--289.
* ↑ B\"ockenhauer, 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. {\mathbf 294}, Amer. Math. Soc., 95--131. math.OA/0006114.
* ↑ B\"ockenhauer, J. and Evans, D. E. (2001). Modular invariants and subfactors. in Mathematical Physics in Mathematics and Physics (ed. R. Longo), The Fields Institute Communications {\mathbf 30}, Providence, Rhode Island: AMS Publications, 11--37. math.OA/0008056.
* ↑ B\"ockenhauer, J., Evans, D. E. and Kawahigashi, Y. (1999). On $\alpha$-induction, chiral generators and modular invariants for subfactors. Communications in Mathematical Physics , {\mathbf 208}, 429--487. math.OA/9904109.
* ↑ B\"ockenhauer, J., Evans, D. E. and Kawahigashi, Y. (2000). Chiral structure of modular invariants for subfactors. Communications in Mathematical Physics , {\mathbf 210}, 733--784. math.OA/9907149.
* ↑ B\"ockenhauer, J., Evans, D. E. and Kawahigashi, Y. (2001). Longo-Rehren subfactors arising from $\alpha$-induction. Publications of the RIMS, Kyoto University , {\mathbf 37}, 1--35. math.OA/0002154.
* ↑ de Boer, J. and Goeree, J. (1991). Markov traces and II$_{1}$ factors in conformal field theory. Communications in Mathematical Physics , {\mathbf 139}, 267--304.
* ↑ Bongaarts, P. J. M. (1970). The electron-positron field, coupled to external electromagnetic potentials as an elementary $C^{*}$-algebra theory. Annals of Physics , {\mathbf 56}, 108--138.
* ↑ Bratteli, O. (1972). Inductive limits of finite dimensional $C^{*}$-algebras. Transactions of the American Mathematical Society , {\mathbf 171}, 195--234.
* ↑ Brunetti, R., Guido, D. and Longo, R. (1993). Modular structure and duality in conformal quantum field theory. Communications in Mathematical Physics , {\mathbf 156}, 201--219.
* ↑ Brunetti, R., Guido, D. and Longo, R. (1995). Group cohomology, modular theory and space-time symmetries. Reviews in Mathematical Physics , {\mathbf 7} 57--71.
* ↑ Buchholz, D., Doplicher, S., Longo, R. and Roberts, J. E. (1993). Extensions of automorphisms and gauge symmetries. Communications in Mathematical Physics , {\mathbf 155}, 123--134.
* ↑ 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.) , {\mathbf B5}, 20--56.
* ↑ Buchholz, D. and Schulz-Mirbach, H. (1990). Haag duality in conformal quantum field theoery, Reviews in Mathematical Physics , {\mathbf 2} 105--125.
* ↑ Camp, W., and Nicoara, R. (preprint 2007). Subfactors and Hadamard matrices. arXiv:0704.1128.
* ↑ Cappelli, A., Itzykson, C. and Zuber, J.-B. (1987). The $A$-$D$-$E$ classification of minimal and $A_{1}^{(1)}$ conformal invariant theories. Communications in Mathematical Physics , {\mathbf 113}, 1--26.
* ↑ 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 , {\mathbf 45}, 259--267.
* ↑ Carpi, S. (2003). The Virasoro algebra and sectors with infinite statistical dimension. Annales Henri Poincar\'e , {\mathbf 4}, 601--611. math.OA/0203027.
* ↑ Carpi, S. (2004). On the representation theory of Virasoro nets. Communications in Mathematical Physics , {\mathbf 244}, 261--284. math.OA/0306425.
* ↑ Carpi, S. (2005). Intersecting Jones projections. International Journal of Mathematics , {\mathbf 16}, 687--691. math.OA/0412457.
* ↑ Carpi, S. and Conti, R. (2001). Classification of subsystems for local nets with trivial superselection structure. Communications in Mathematical Physics , {\mathbf 217}, 89--106.
* ↑ Carpi, S. and Conti, R. (2005). Classification of subsystems for graded-local nets with trivial superselection structure. Communications in Mathematical Physics . {\mathbf 253}, 423--449. math.OA/0312033.
* ↑ Carpi, S., Kawahigashi, Y. and Longo, R. (in press). Structure and classification of superconformal nets. Annales Henri Poincar\'e . arXiv:0705.3609.
* ↑ Carpi, S. and Weiner, M. (2005). On the uniqueness of diffeomorphism symmetry in Conformal Field Theory. Communications in Mathematical Physics , {\mathbf 258}, 203--221. math.OA/0407190.
* ↑ Ceccherini, T. (1996). Approximately inner and centrally free commuting squares of type $II_{1}$ factors and their classification. Journal of Functioanl Analysis , {\mathbf 142}, 296--336.
* ↑ Chen, J. (1993). The Connes invariant $\chi (M)$ and cohomology of groups. Ph. D. dissertation at University of California, Berkeley.
* ↑ Choda, M. (1989). Index for factors generated by Jones' two sided sequence of projections. Pacific Journal of Mathematics , {\mathbf 139}, 1--16.
* ↑ Choda, M. (1991). Entropy for $*$-endomorphisms and relative entropy for subalgebras. Journal of Operator Theory , {\mathbf 25}, 125--140.
* ↑ Choda, M. (1992). Entropy for canonical shift. Transactions of the American Mathematical Society , {\mathbf 334}, 827--849.
* ↑ Choda, M. (1993). Duality for finite bipartite graphs (with applications to II$_{1}$ factors). Pacific Journal of Mathematics , {\mathbf 158}, 49--65.
* ↑ Choda, M. (1994). Square roots of the canonical shifts. Journal of Operator Theory , {\mathbf 31}, 145--163.
* ↑ Choda, M. (1994). Extension algebras via $*$-endomorphisms. in {\em Subfactors --- Proceedings of the Taniguchi Symposium, Katata ---}, (ed. H. Araki, et al.), World Scientific, 105--128.
* ↑ Choda, M. and Hiai, F. (1991). Entropy for canonical shifts. II. Publications of the RIMS, Kyoto University , {\mathbf 27}, 461--489.
* ↑ Choda, M. and Kosaki, H. (1994). Strongly outer actions for an inclusion of factors. Journal of Functional Analysis , {\mathbf 122}, 315--332.
* ↑ Christensen, E. (1979). Subalgebras of a finite algebra. Mathematische Annalen , {\mathbf 243}, 17--29.
* ↑ Combes, F. (1968). Poids sur une $C^{*}$-alg\`ebre. {\em Journal de Math\'ematiques Pures et Appliqu\'ees}, {\mathbf 47}, 57--100.
* ↑ Connes, A. (1973). Une classification des facteurs de type III. Annales Scientifiques de l'\'Ecole Normale Sup\'erieure , {\mathbf 6}, 133--252.
* ↑ Connes, A. (1975). Outer conjugacy classes of automorphisms of factors. Annales Scientifiques de l'\'Ecole Normale Sup\'erieure , {\mathbf 8}, 383--419.
* ↑ Connes, A. (1975). Hyperfinite factors of type III-0 and Krieger's factors. Journal of Functional Analysis , {\mathbf 18}, 318--327.
* ↑ Connes, A. (1975). Sur la classification des facteurs de type II. {\em Comptes Rendus de l'Academie des Sciences, S\'erie I, Math\'ematiques}, {\mathbf 281}, 13--15.
* ↑ Connes, A. (1975). A factor not antiisomorphic to itself. Annals of Mathematics , {\mathbf 101}, 536--554.
* ↑ Connes, A. (1976). Classification of injective factors. Annals of Mathematics , {\mathbf 104}, 73--115.
* ↑ Connes, A. (1976). Outer conjugacy of automorphisms of factors. Symposia Mathematica , {\mathbf XX}, 149--160.
* ↑ Connes, A. (1976). On the classification of von Neumann algebras and their automorphisms. Symposia Mathematica , {\mathbf XX}, 435--478.
* ↑ Connes, A. (1977). Periodic automorphisms of the hyperfinite factor of type II$_{1}$. Acta Scientiarum Mathematicarum , {\mathbf 39}, 39--66.
* ↑ Connes, A. (1978). On the cohomology of operator algebras. Journal of Functional Analysis , {\mathbf 28}, 248--253.
* ↑ Connes, A. (1979). Sur la th\'eorie non commutative de l'integration. Springer Lecture Notes in Math. , {\mathbf 725}, 19--143.
* ↑ Connes, A. (1980). $C^{*}$-algebres et geom\`etrie diff\'erentielle. {\em Comptes Rendus de l'Academie des Sciences, S\'erie I, Math\'ematiques}, 559--604.
* ↑ Connes, A. (1980). Spatial theory of von Neumann algebras. Journal of Functional Analysis , {\mathbf 35} (1980), 153--164.
* ↑ Connes, A. (1981). An analogue of the Thom isomorphism for crossed products of a $C^{*}$-algebra by an action of ${\mathbf {R} }$. Advances in Mathematics , {\mathbf 39}, 311--355.
* ↑ Connes, A. (1982). Foliations and Operator Algebras. {\em Proceedings of Symposia in Pure Mathematics. ed. R. V. Kadison}, {\mathbf 38}, 521--628.
* ↑ Connes, A. (1982). Classification des facteurs. Proceedings of the Symposia in Pure Mathematics (II) , {\mathbf 38}, 43--109.
* ↑ Connes, A. (1985). Non-commutative differential geometry I--II. Publication Math\'ematiques IHES , {\mathbf 62}, 41--144.
* ↑ Connes, A. (1985). Factors of type III-1, property $L'_{\lambda }$ and closure of inner automorphisms. Journal of Operator Theory , {\mathbf 14}, 189--211.
* ↑ Connes, A. (1985). Non Commutative Differential Geometry, Chapter II: De Rham homology and non commutative algebra. Publication Math\'ematiques IHES , {\mathbf 62}, 257--360.
* ↑ Connes, A. (1994). Noncommutative geometry. Academic Press .
* ↑ Connes, A. and Evans, D. E. (1989). Embeddings of $U(1)$-current algebras in non-commutative algebras of classical statistical mechanics. {\em Communications in Mathematical Physics}, {\mathbf 121}, 507--525.
* ↑ Connes, A. and Higson, N. (1990). D\'eformations, morphismes asymptotiques et $K$-th\'eorie bivariante. {\em Comptes Rendus de l' Academie des Sciences, S\'erie I, Math\'ematiques}, {\mathbf 311}, 101--106.
* ↑ Connes, A. and Karoubi, M. (1988). Caractere multiplicatif d'un module de Fredholm. $K$-theory , {\mathbf 2} 431--463.
* ↑ Connes, A. and Krieger, W. (1977). Measure space automorphism groups, the normalizer of their full groups, and approximate finiteness. Journal of Functional Analysis , {\mathbf 24}, 336--352.
* ↑ Connes, A. and Rieffel, M. (1985). Yang-Mills for non-commutative tori. Contemporary Mathematics , {\mathbf 62}, 237--265.
* ↑ Connes, A. and Skandalis, G. (1984). The longitudinal index theorem for foliations. Publications of the RIMS, Kyoto University , {\mathbf 20}, 1139--1183.
* ↑ Connes, A. and St\"ormer, E. (1975). Entropy for automorphisms of $II_{1}$ von Neumann algebras. Acta Mathematica , {\mathbf 134}, 289--306.
* ↑ Connes, A. and Takesaki, M. (1977). The flow of weights on factors of type III. Tohoku Mathematical Journal , {\mathbf 29}, 73--555.
* ↑ Conti, R., Doplicher, S., and Roberts, J. E. (2001). Superselection theory for subsystems. Communications in Mathematical Physics , {\mathbf 218}, 263--281.
* ↑ Conti, R. and Pinzari, C. (1996). Remarks on the index of endomorphisms of Cuntz algebras. Journal of Functional Analysis , {\mathbf 142}, 369--405.
* ↑ Coquereaux, R. (2005) The $A_{2}$ Ocneanu quantum groupoid. in Algebraic structures and their representations , Contemporary Mathematics , {\mathbf 376}, 227--247. hep-th/0311151.
* ↑ 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 , {\mathbf 42}, 216--258.
* ↑ Coquereaux, R. and Schieber, G. (2003). Determination of quantum symmetries for higher ADE systems from the modular T matrix. Journal of Mathematical Physics , {\mathbf 44}, 3809--3837. hep-th/0203242. \ bibitem{Cn} Cuntz, J. (1977). Simple $C^{*}$-algebras generated by isometries. Communications in Mathematical Physics , {\mathbf 57}, 173--185.
* ↑ Cuntz, J. (1981). $K$-theory for certain $C^{*}$-algebras. Annals of Mathematics , {\mathbf 113}, 181--197.
* ↑ Cuntz, J. (1984). $K$-theory and $C^{*}$-algebras. Lecture Notes in Mathematics, Springer-Verlag , {\mathbf 1046}.
* ↑ Cuntz, J. (1981). A class of $C^{*}$-algebras and topological Markov chains II. Reducible Markov chains and the $Ext$ functor for $C^{*}$-algebras. Inventiones Mathematica , {\mathbf 63}, 25--40.
* ↑ Cuntz, J. and Krieger, W. (1980). A class of $C^{*}$-algebras and topological Markov chains. Inventiones Mathematicae , {\mathbf 56}, 251--268.
* ↑ Cvetkovi\'c, D., Doob, M. and Gutman, I. (1982). On graphs whose spectral radius does not exceed $(2+{\sqrt {5}})^{1/2}$. Ars Combinatoria , {\mathbf 14}, 225--239.
* ↑ D'Antoni, C., Fredenhagen, K. and K\"oster, S. (preprint 2003). Implementation of conformal covariance by diffeomorphism symmetry. math-ph/0312017.
* ↑ D'Antoni, C., Longo, R. and Radulescu, F. (2001). Conformal nets, maximal temperature and models from free probability. Journal of Operator Theory , {\mathbf 45}, 195--208.
* ↑ Date, E., Jimbo, M., Kuniba, A., Miwa, T. and Okado, M. (1988). Exactly solvable SOS models II: Proof of the star-triangle relation and combinatorial identities. Advanced Studies in Pure Mathematics , {\mathbf 16}, 17--122.
* ↑ Date, E., Jimbo, M., Miwa, T. and Okado, M. (1987). Solvable lattice models. Theta functions --- Bowdoin 1987, Part 1 , Proceedings of Symposia in Pure Mathematics Vol. 49, American Mathematical Society, Providence, R.I., pp. 295--332.
* ↑ David, M. C. (1996). Paragroupe d'Adrian Ocneanu et alg\`ebre de Kac. Pacific Journal of Mathematics , {\mathbf 172}, 331--363.
* ↑ Degiovanni, P. (1990). ${\mathbf {Z} }/N{\mathbf {Z} }$ conformal field theories. Communications in Mathematical Physics , {\mathbf 127}, 71--99.
* ↑ Degiovanni, P. (1992). Moore and Seiberg's equations and 3D toplogical field theory. {\mathbf 145}, 459--505.
* ↑ Di Francesco, P. (1992). Integrable lattice models, graphs, and modular invariant conformal field theories. International Journal of Modern Physics A , {\mathbf 7}, 407--500.
* ↑ Di Francesco, P., Mathieu, P. and S\'en\'echal, D. (1996). Conformal Field Theory. Springer-Verlag, New York.
* ↑ Di Francesco, P., Saleur, H. and Zuber, J.-B. (1987). Modular invariance in non-minimal two-dimensional conformal field theories. Nuclear Physics , {\mathbf B285}, 454--480.
* ↑ Di Francesco, P. and Zuber, J.-B. (1990). $SU(N)$ lattice integrable models associated with graphs. Nuclear Physics B , {\mathbf 338}, 602--646.
* ↑ Di Francesco, P. and Zuber, J.-B. (1990). $SU(N)$ lattice integrable models and modular invariance. in Recent Developments in Conformal Field Theories, Trieste, 1989 , World Scientific, 179--215.
* ↑ Dijkgraaf, R., Pasquier, V. and Roche, Ph. (1990). Quasi Hopf algebras, group cohomology and orbifold models. Nuclear Physics B(Proc. Suppl.) , {\mathbf 18}, 60--72.
* ↑ Dijkgraaf, R., Pasquier, V. and Roche, Ph. (1991). Quasi-quantum groups related to orbifold models. {\em Proceedings of the International Colloquium on Modern Quantum Field Theory}, World Scientific, Singapore, 375--383.
* ↑ Dijkgraaf, R., Vafa, C., Verlinde, E. and Verlinde, H. (1989). The operator algebra of orbifold models. Communications in Mathematical Physics , {\mathbf 123}, 485--526.
* ↑ Dijkgraaf, R. and Witten, E. (1990). Topological gauge theories and group cohomology. Communications in Mathematical Physics , {\mathbf 129}, 393--429.
* ↑ Dixmier, J. (1964). Les $C^{*}$-algebras et leurs repr\'esentations. Gauthier-Villars .
* ↑ Dixmier, J. (1967). On some $C^{*}$-algebras considered by Glimm. Journal of Functional Analysis , {\mathbf 1}, 182--203.
* ↑ Dixmier, J. (1969). {\em Les alg\`ebres d'op\'erateurs dans l'espace Hilbertien. (Alg\`ebres de von Neumann.)} 2nd ed. Gauthier Villars, Paris.
* ↑ Dixmier, J. (1981). Von Neumann Algebras. North-Holland .
* ↑ Dixmier, J. and C. Lance (1969). Deux nouveaux facteurs de type II. Inventiones Mathematicae , {\mathbf 7}, 226--234.
* ↑ Dixon, L., Harvey, J. A., Vafa, C. and Witten, E. (1985). Strings on orbifolds. Nuclear Physics B , {\mathbf 261}, 678--686.
* ↑ Dixon, L., Harvey, J. A., Vafa, C. and Witten, E. (1986). Strings on orbifolds. Nuclear Physics B , {\mathbf 274}, 285--314.
* ↑ Dong, C. and Xu, F. (2006). Conformal nets associated with lattices and their orbifolds. Advances in Mathematics , {\mathbf 206}, 279--306. math.OA/0411499.
* ↑ Doplicher, S., Haag, R. and Roberts, J. E. (1969). Fields, observables and gauge transformations II. Communications in Mathematical Physics , {\mathbf 15}, 173--200.
* ↑ Doplicher, S., Haag, R. and Roberts, J. E. (1971, 74). Local obsevables and particle statistics, I,II. Communications in Mathematical Physics , {\mathbf 23}, 199--230 and {\mathbf 35}, 49--85.
* ↑ Doplicher, S. and Longo, R. (1984). Standard and split inclusions of von Neumann algebras. Inventiones Mathematicae , {\mathbf 75}, 493--536. bibitem{DP} Doplicher, S. and , Piacitelli, G. (preprint 2002). Any compact group is a gauge group. hep-th/0204230.
* ↑ Doplicher, S., Pinzari, C. and Roberts, J. E. (2001). An algebraic duality theory for multiplicative unitaries. International Journal of Mathematics , {\mathbf 12}, 415--459.
* ↑ Doplicher, S. and Roberts, J. E. (1989). Endomorphisms of Failed to parse (unknown function "\sp"): {\displaystyle C\sp *} -algebras, cross products and duality for compact groups. Annals of Mathematics , {\mathbf 130}, 75--119.
* ↑ Doplicher, S. and Roberts, J. E. (1989). A new duality theory for compact groups. Inventiones Mathematica , {\mathbf 98}, 157--218.
* ↑ Drinfel$'$d, V. G. (1986). Quantum groups. Proc. ICM-86, Berkeley , 798--820.
* ↑ Dunford, N. and Schwartz, J. T. (1958). Linear Operators Volume I. Interscience.
* ↑ Durhuus, B., Jakobsen, H. P. and Nest, R. (1993). Topological quantum field theories from generalized $6j$-symbols. Reviews in Mathematical Physics , {\mathbf 5}, 1--67.
* ↑ Elliott, G. A. (1976). On the classification of inductive limits of sequences of semisimple finite-dimensional algebras. Journal of Algebra , {\mathbf 38}, 29--44.
* ↑ Enock, M. (1998). Inclusions irr\'educibles de facteurs et unitaires multiplicatifs, II. Journal of Functional Analysis , {\mathbf 154}, 67--109.
* ↑ Enock, M. (1999). Sous-facteurs interm\'ediaires et groupes quantiques mesur\'es. Journal of Operator Theory , {\mathbf 42}, 305--330.
* ↑ Enock, M. (2000). Inclusions of von Neumann algebras and quantum groupoids, II. Journal of Functional Analysis , {\mathbf 178}, 156--225.
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* ↑ Kawahigashi, Y. (1992). Automorphisms commuting with a conditional expectation onto a subfactor with finite index. Journal of Operator Theory , {\mathbf 28}, 127--145.
* ↑ Kawahigashi, Y. (1992). Exactly solvable orbifold models and subfactors. Functional Analysis and Related Topics , Lecture Notes in Mathematics, Springer, {\mathbf 1540}, 127--147.
* ↑ Kawahigashi, Y. (1993). Centrally trivial automorphisms and an analogue of Connes's $\chi (M)$ for subfactors. Duke Mathematical Journal , {\mathbf 71}, 93--118.
* ↑ Kawahigashi, Y. (1994). Paragroup and their actions on subfactors. in {\em Subfactors --- Proceedings of the Taniguchi Symposium, Katata ---}, (ed. H. Araki, et al.), World Scientific, 64--84.
* ↑ Kawahigashi, Y. (1995). On flatness of Ocneanu's connections on the Dynkin diagrams and classification of subfactors. Journal of Functional Analysis , {\mathbf 127}, 63--107.
* ↑ Kawahigashi, Y. (1995). Orbifold subfactors, central sequences and the relative Jones invariant $\kappa$. International Mathematical Research Notices , 129--140.
* ↑ Kawahigashi, Y. (1995). Classification of paragroup actions on subfactors. Publications of the RIMS, Kyoto University , {\mathbf 31}, 481--517.
* ↑ Kawahigashi, Y. (1996). Paragroups as quantized Galois groups of subfactors. Sugaku Expositions , {\mathbf 9}, 21--35.
* ↑ Kawahigashi, Y. (1997). Classification of approximately inner automorphisms of subfactors. Mathematische Annalen , {\mathbf 308}, 425--438.
* ↑ Kawahigashi, Y. (1997). Quantum doubles and orbifold subfactors. in Operator Algebras and Quantum Field Theory (ed. S. Doplicher, et al.), International Press, 271--283.
* ↑ Kawahigashi, Y. (1998). Subfactors and paragroup theory. in Operator Algebras and Operator Theory (ed. L. Ge, et al.), Contemporary Mathematics , {\mathbf 228}, 179--188.
* ↑ Kawahigashi, Y. (1999). Quantum Galois correspondence for subfactors. Journal of Functional Analysis , {\mathbf 167}, 481--497.
* ↑ Kawahigashi, Y. (2004). Braiding and nets of factors on the circle. in Operator Algebras and Applications (ed. H. Kosaki), Advanced Studies in Pure Mathematics {\mathbf 38}, 219--228.
* ↑ Kawahigashi, Y. (2001). Braiding and extensions of endomorphisms of subfactors. in Mathematical Physics in Mathematics and Physics (ed. R. Longo), The Fields Institute Communications {\mathbf 30}, Providence, Rhode Island: AMS Publications, 261--269.
* ↑ Kawahigashi, Y. (2002). Generalized Longo-Rehren subfactors and $\alpha$-induction. Communications in Mathematical Physics , {\mathbf 226}, 269--287. math.OA/0107127.
* ↑ Kawahigashi, Y. (2003). Conformal quantum field theory and subfactors. Acta Mathematica Sinica , {\mathbf 19}, 557--566.
* ↑ Kawahigashi, Y. (2003). Classification of operator algebraic conformal field theories. "Advances in Quantum Dynamics", Contemporary Mathematics , {\mathbf 335}, 183--193. math.OA/0211141.
* ↑ Kawahigashi, Y. (2005). Subfactor theory and its applications --- operator algebras and quantum field theory ---. "Selected Papers on Differential Equations" , Amer. Math. Soc. Transl. {\mathbf 215}, Amer. Math. Soc., 97--108.
* ↑ Kawahigashi, Y. (2005). Topological quantum field theories and operator algebras. Quantum Field Theory and Noncommutative Geometry , Lecture Notes in Physics, Springer, {\mathbf 662}, 241--253. math.OA/0306112.
* ↑ Kawahigashi, Y. (2005). Classification of operator algebraic conformal field theories in dimensions one and two. XIVth International Congress on Mathematical Physics , World Scientific, 476--485. math-ph/0308029.
* ↑ Kawahigashi, Y. (preprint 2007). Conformal field theory and operator algebras. arXiv:0704.0097.
* ↑ Kawahigashi, Y. (preprint 2007). Superconformal field theory and operator algebras.
* ↑ Kawahigashi, Y. and Longo, R. (2004). Classification of Local Conformal Nets. Case $c<1$. Annals of Mathematics , {\mathbf 160}, 493--522. math-ph/0201015.
* ↑ Kawahigashi, Y. and Longo, R. (2004). Classification of two-dimensional local conformal nets with $c<1$ and 2-cohomology vanishing for tensor categories. Communications in Mathematical Physics , {\mathbf 244}, 63--97. math-ph/0304022.
* ↑ Kawahigashi, Y. and Longo, R. (2005).Noncommutative spectral invariants and black hole entropy. Communications in Mathematical Physics , {\mathbf 257}, 193--225. math-ph/0405037.
* ↑ Kawahigashi, Y. and Longo, R. (2006). Local conformal nets arising from framed vertex operator algebras. Advances in Mathematics , {\mathbf 206}, 729--751. math.OA/0407263.
* ↑ Kawahigashi, Y., Longo, R. and M\"uger, M. (2001). Multi-interval subfactors and modularity of representations in conformal field theory. Communications in Mathematical Physics , {\mathbf 219}, 631--669. math.OA/9903104.
* ↑ Kawahigashi, Y., Longo, R., Pennig, U. and Rehren, K.-H. (2007). The classification of non-local chiral CFT with $c<1$. Communications in Mathematical Physics , {\mathbf 271}, 375--385. math.OA/0505130.