# PlanetPhysics/Bibliography for Physical Mathematics of Operator Algebras and AQFT K to Z

\begin{thebibliography} {299} </ref></references>
* ↑ Kawahigashi, Y., Sato, N. and Wakui, M. (2005). $(2+1)$-dimensional topological quantum field theory from subfactors and Dehn surgery formula for $3$-manifold invariants. Advances in Mathematics , {\mathbf 195}, 165-179.
* ↑ Kazhdan, V. and Lusztig, G. (1994). Tensor structures arising from affine Lie algebras. IV, Journal of the American Mathematical Society , {\mathbf 7}, 383--453.
* ↑ Kirby, R. (1978). A calculus of farmed links in $S^{3}$. Inventiones Mathematicae , {\mathbf 45}, 35--56.
* ↑ Kirby, R. and Melvin, P. (1990). On the $3$-manifold invariants of Witten and Reshetikhin--Turaev. Inventiones Mathematicae , {\mathbf 105}, 473--545.
* ↑ Kirillov, A. Jr. and Ostrik, V. (2002). On $q$-analog of McKay correspondence and ADE classification of $sl^{(2)}$ conformal field theories. Advances in Mathematics , {\mathbf 171}, 183--227. math.QA/0101219.
* ↑ Kirillov, A. N. and Reshetikhin, N. Yu. (1988). Representations of the algebra $U_{q}(sl_{2})$, $q$-orthogonal polynomials and invariants for links. Infinite dimensional Lie algebras and groups , (Ka\v c, V. G., ed.), Advanced Series in Mathematical Physics, vol. 7, 285--339.
* ↑ Knizhnik, V. and Zamolodchikov, A. (1984). Current algebra and Weiss-Zumino models in two dimensions. Nuclear Physics B , {\mathbf 247}, 83--103.
* ↑ Kodiyalam, V. and Sunder, V. S. (2001). Spectra of principal graphs. International Journal of Mathematics , {\mathbf 12}, 203--210.
* ↑ Kodiyalam, V. and Sunder, V. S. (2001). Flatness and fusion coefficients. Pacific Journal of Mathematics , {\mathbf 201}, 177--204.
* ↑ Kodiyalam, V. and Sunder, V. S. (2001). Topological quantum field theories from subfactors. Chapman \& Hall/CRC, Research Notes in Mathematics, {\mathbf 423}.
* ↑ Kohno, T. (1987). Monodromy representations of braid groups and Yang--Baxter equations. Annales de l'Institut Fourier, Grenoble , {\mathbf 37,4}, 139--160.
* ↑ Kohno, T. (1992). Topological invariants for $3$-manifolds using representations of mapping class groups I. Topology , {\mathbf 31}, 203--230.
* ↑ Kohno, T. (1992). Three-manifold invariants derived from conformal field theory and projective representations of modular groups. International Journal of Modern Physics , {\mathbf 6}, 1795--1805.
* ↑ Kosaki, H. (1986). Extension of Jones' theory on index to arbitrary factors. Journal of Functional Analysis , {\mathbf 66}, 123--140.
* ↑ Kosaki, H. (1989). Characterization of crossed product (properly infinite case). Pacific Journal of Mathematics , {\mathbf 137}, 159--167.
* ↑ Kosaki, H. (1990). Index theory for type III factors. in {\em Mappings of operator algebras, Proceedings of U.S.-Japan Seminar}, (ed. H. Araki and R. V. Kadison), Birkh\"auser, 129--139.
* ↑ Kosaki, H. (1993). Automorphisms in the irreducible decompositions of sectors. Quantum and non-commutative analysis , (ed. H. Araki et al.), Kluwer Academic, 305--316.
* ↑ Kosaki, H. (1994). AFD factor of type III$_{0}$ with many isomorphic index 3 subfactors. Journal of Operator Theory , {\mathbf 32}, 17--29.
* ↑ Kosaki, H. (1994). Some remarks on automorphisms for inclusions of type III factors. in Subfactors --- Proceedings of the Taniguchi Symposium, Katata --- , (ed. H. Araki, et al.), World Scientific, 153--171.
* ↑ Kosaki, H. (1996). Sector theory and automorphisms for factor-subfactor pairs. Journal of the Mathematical Society of Japan , {\mathbf 48}, 427--454.
* ↑ Kosaki, H. and Loi, P. H. (1995). A remark on non-splitting inclusions of type III$_{1}$ factors. International Journal of Mathematics , {\mathbf 6}, 581--586.
* ↑ Kosaki, H. and Longo, R. (1992). A remark on the minimal index of subfactors. Journal of Functional Analysis , {\mathbf 107}, 458--470.
* ↑ Kosaki, H., Munemasa, A. and Yamagami, S. (1997). On fusion algebras associated to finite group actions. Pacific Journal of Mathematics , {bf 177}, 269--290.
* ↑ Kosaki, H. and Yamagami, S. (1992). Irreducible bimodules associated with crossed product algebras. International Journal of Mathematics , {\mathbf 3}, 661--676.
* ↑ K\"oster, S. (2002). Conformal transformations as observables. Letters in Mathematical Physics , {\mathbf 61}, 187--198.
* ↑ K\"oster, S. (preprint 2003). Absence of stress energy tensor in CFT$_{2}$ models. math-ph/0303053.
* ↑ K\"oster, S. (2004). Local nature of coset models. Reviews in Mathematical Physics , {\mathbf 16}, 353--382. math-ph/0303054.
* ↑ K\"oster, S. (preprint 2003). Structure of coset models. math-ph/0308031.
* ↑ Kostov, I. (1988). Free field presentation of the $A_{n}$ coset models on the torus. Nuclear Physics B , {\mathbf 300}, 559--587.
* ↑ Kramers, H. A. and Wannier, G. H. (1941). Statistics of the two dimensional ferromagnet part 1. Physical Review , {\mathbf 60}, 252--262.
* ↑ Kuik, R. (1986). On the $q$-state Potts model by means of non-commutative algebras. Ph.D. Thesis Groningen.
* ↑ Kulish, P. and Reshetikhin, N. (1983). Quantum linear problem for the sine-Gordon equation and higher representations. Journal of Soviet Mathematics , {\mathbf 23}, 2435--2441.
* ↑ Kuniba, A., Akutsu, Y. and Wadati, M. (1986). Virasoro algebra, von Neumann algebra and critical eight vertex SOS model. Journal of Physics Society of Japan , {\mathbf 55}, 3285--3288.
* ↑ Landau, Z. (2001). Fuss-Catalan algebras and chains of intermediate subfactors. Pacific Journal of Mathematics , {\mathbf 197}, 325--367.
* ↑ Landau, Z. (2002). Exchange relation planar algebras. Journal of Functional Analysis , {\mathbf 195}, 71--88.
* ↑ Lickorish, W. (1988). Polynomials for links. Bulletin of the American Mathematical Society , {\mathbf 20}, 558--588.
* ↑ Loi, P. H. (1988). On the theory of index and type III factors. Thesis, Pennsylvania State University.
* ↑ Loi, P. H. (1996). On automorphisms of subfactors. Journal of Functional Analysis , {\mathbf 141}, 275--293.
* ↑ Loi, P. H. (1994). On the derived tower of certain inclusions of type III$_{\lambda }$ factors of index 4. Pacific Journal of Mathematics , {\mathbf 165}, 321--345.
* ↑ Loi, P. H. (1994). Remarks on automorphisms of subfactors. Proceedings of the American Mathematical Society , {\mathbf 121}, 523--531.
* ↑ Loi, P. H. (1997). Periodic and strongly free automorphisms on inclusions of type III$_{\lambda }$ factors. International Journal of Mathematics , {\mathbf 8}, 83--96.
* ↑ Loi, P. H. (1998). A structural result of irreducible inclusions of type III$_{\lambda }$ factors. Proceedings of the American Mathematical Society , {\mathbf 126}, 2651--2662.
* ↑ Loi, P. H. (1998). Commuting squares and the classification of finite depth inclusions of AFD type III$_{\lambda }$ factors, $\lambda \in (0,1)$. Publications of the RIMS, Kyoto University , {\mathbf 34}, 115--122.
* ↑ Loke, T. (1994). Operator algebras and conformal field theory of the discrete series representations of Diff$(S^{1})$. Thesis, University of Cambridge .
* ↑ Longo, R. (1978) A simple proof of the existence of modular automorphisms in approximately finite dimensional von Neumann algebras. Pacific Journal of Mathematics , {\mathbf 75}, 199--205.
* ↑ Longo, R. (1979). Automatic relative boundedness of derivations in $C^{*}$-algebras. Journal of Functional Analysis , {\mathbf 34}, 21--28.
* ↑ Longo, R. (1984). Solution of the factorial Stone-Weierstrass conjecture. An application of the theory of standard split $W^{*}$-inclusions. Inventiones Mathematicae , {\mathbf 76}, 145--155.
* ↑ Longo, R. (1987). Simple injective subfactors. Advances in Mathematics , {\mathbf 63}, 152--171.
* ↑ Longo, R. (1989). Index of subfactors and statistics of quantum fields, I. Communications in Mathematical Physics , {\mathbf 126}, 217--247.
* ↑ Longo, R. (1990). Index of subfactors and statistics of quantum fields II. Communications in Mathematical Physics , {\mathbf 130}, 285--309.
* ↑ Longo, R. (1992). Minimal index and braided subfactors. Journal of Functional Analysis , {\mathbf 109}, 98--112.
* ↑ Longo, R. (1994). A duality for Hopf algebras and for subfactors I. Communications in Mathematical Physics , {\mathbf 159}, 133--150.
* ↑ Longo, R. (1994). Problems on von Neumann algebras suggested by quantum field theory. in Subfactors --- Proceedings of the Taniguchi Symposium, Katata --- , (ed. H. Araki, et al.), World Scientific, 233--241.
* ↑ Longo, R. (1997). An analogue of the Kac-Wakimoto formula and black hole conditional entropy. Communications in Mathematical Physics , {\mathbf 186}, 451--479.
* ↑ Longo, R. (1999). On the spin-statistics relation for topological charges. in Operator Algebras and Quantum Field Theory (ed. S. Doplicher, et al.), International Press, 661--669.
* ↑ Longo, R. (2001). Notes for a quantum index theorem. Communications in Mathematical Physics , {\mathbf 222}, 45--96.
* ↑ Longo, R. (2003). Conformal subnets and intermediate subfactors. Communications in Mathematical Physics , {\mathbf 237}, 7--30. math.OA/0102196.
* ↑ Longo, R. and Rehren, K.-H. (1995). Nets of subfactors. Reviews in Mathematical Physics , {\mathbf 7}, 567--597.
* ↑ Longo, R. and Rehren, K.-H. (2004). Local fields in boundary CFT. Reviews in Mathematical Physics , {\mathbf 16}, 909--960. math-ph/0405067.
* ↑ Longo, R. and Rehren, K.-H. (preprint 2007). How to remove the boundary. arXiv:0712.2140.
* ↑ Longo, R. and Roberts, J. E. (1997). A theory of dimension. $K$-theory , {\mathbf 11}, 103--159.
* ↑ Longo, R. and Xu, F. (2004). Topological sectors and a dichotomy in conformal field theory. Communications in Mathematical Physics , {\mathbf 251}, 321--364. math.OA/0309366.
* ↑ Markov, A. (1935). \"Uber de freie Aquivalenz geschlossener Z\"opfe. Rossiiskaya Akademiya Nauk, Matematicheskii Sbornik , {\mathbf 1}, 73--78.
* ↑ Masuda, T. (1997). An analogue of Longo's canonical endomorphism for bimodule theory and its application to asymptotic inclusions. International Journal of Mathematics , {\mathbf 8}, 249--265.
* ↑ Masuda, T. (1999). Classification of actions of discrete amenable groups on strongly amenable subfactors of type $III_{\lambda }$. Proceedings of the American Mathematical Society , {\mathbf 127}, 2053--2057.
* ↑ Masuda, T. (1999). Classification of strongly free actions of discrete amenable groups on strongly amenable subfactors of type $III_{0}$. Pacific Journal of Mathematics , {\mathbf 191}, 347--357.
* ↑ Masuda, T. (2000). Generalization of Longo-Rehren construction to subfactors of infinite depth and amenability of fusion algebras. Journal of Functional Analysis , {\mathbf 171}, 53--77.
* ↑ Masuda, T. (2001). Extension of automorphisms of a subfactor to the symmetric enveloping algebra. International Journal of Mathematics , {\mathbf 12}, 637--659.
* ↑ Masuda, T. (in press). Classification of approximately inner actions of discrete amenable groups on strongly amenable subfactors. International Journal of Mathematics ,
* ↑ Masuda, T. (2003).Notes on group actions on subfactors. Journal of the Mathematical Society of Japan , {\mathbf 55}, 1--11.
* ↑ Masuda, T. (2003). On non-strongly free automorphisms of subfactors of type III$_{0}$. Canadian Mathematical Bulletin , {\mathbf 46}, 419--428.
* ↑ Masuda, T. (2005). An analogue of Connes-Haagerup approach to classification of subfactors of type $III_{1}$. Journal of the Mathematical Society of Japan , {\mathbf 57}, 959--1001.
* ↑ McCoy, B. and Wu, T. (1972). The two dimensional Ising model. Harvard University Press, Cambridge, Massachusetts , {\mathbf 40}.
* ↑ McDuff, D. (1969). Uncountably many $II_{1}$ factors. Annals of Mathematics , {\mathbf 90}, 372--377.
* ↑ McDuff, D. (1970). Central sequences and the hyperfinite factor. Proceedings of the London Mathematical Society , {\mathbf 21}, 443--461.
* ↑ Moore, G. and Seiberg, N. (1989). Classical and quantum conformal field theory. Communications in Mathematical Physics , {\mathbf 123}, 177--254.
* ↑ Moore, G. and Seiberg, N. (1989). Naturality in conformal field theory. Nuclear Physics B , {\mathbf 313}, 16--40.
* ↑ M\"uger, M. (1998). Superselection structure of massive quantum field theories in $1+1$ dimensions. Reviews in Mathematical Physics , {\mathbf 10}, 1147--1170.
* ↑ M\"uger, M. (1999). On soliton automorphisms in massive and conformal theories. Reviews in Mathematical Physics , {\mathbf 11}, 337--359.
* ↑ M\"uger, M. (1999). On charged fields with group symmetry and degeneracies of Verlinde's matrix $S$. Annales de l'Institut Henri Poincar\'e. Physique Th\'eorique , {\mathbf 71}, 359--394.
* ↑ M\"uger, M. (2000). Galois theory for braided tensor categories and the modular closure. Advances in Mathematics , {\mathbf 150}, 151--201.
* ↑ M\"uger, M. (2001). Conformal field theory and Doplicher-Roberts reconstruction. in Mathematical Physics in Mathematics and Physics (ed. R. Longo), The Fields Institute Communications {\mathbf 30}, Providence, Rhode Island: AMS Publications, 297--319. math-ph/0008027.
* ↑ M\"uger, M. (2003). From subfactors to categories and topology I. Frobenius algebras in and Morita equivalence of tensor categories. Journal of Pure and Applied Algebra , {\mathbf 180}, 81--157. math.CT/0111204.
* ↑ M\"uger, M. (2003). From subfactors to categories and topology II. The quantum double of subfactors and categories. Journal of Pure and Applied Algebra , {\mathbf 180}, 159--219. math.CT/0111205.
* ↑ M\"uger, M. (in press). On the structure of modular categories. Proceedings of the London Mathematical Society . math.CT/0201017.
* ↑ M\"uger, M. (preprint 2002). Galois extensions of braided tensor categories and braided crossed G-categories. math.CT/0209093.
* ↑ M\"uger, M. (2005). Conformal orbifold theories and braided crossed G-categories Communications in Mathematical Physics , {\mathbf 260}, 727--762. math.QA/0403322.
* ↑ Munemasa, A. and Watatani, Y. (1992). Paires orthogonales de sous-algebres involutives. {\em Comptes Rendus de l'Academie des Sciences, S\'erie I, Math\'ematiques}, {\mathbf 314}, 329--331.
* ↑ Murakami, J. (1987). The Kauffman polynomial of lins and representation theory. Osaka Journal of Mathematics , {\mathbf 24}, 745--758.
* ↑ Murakami, H. (1994). Quantum $SU(2)$-invariants dominate Casson's $SU(2)$-invariant. Mathematical Proceedings of the Cambridge Philosophical Society , {\mathbf 115}, 253--281.
* ↑ Murphy, G. J. (1990). $C^{*}$-Algebras and Operator Theory. Academic Press Incorporated .
* ↑ Murray, F. J. (1990). The rings of operators. Symposia Mathematica ,{\mathbf 50}, 57--60.
* ↑ Murray, F. J. and von Neumann, J. (1936). On rings of operators. Annals of Mathematics , {\mathbf 37}, 116--229.
* ↑ Murray, F. J. and von Neumann, J. (1937). On rings of operators II. Transactions of the American Mathematical Society , {\mathbf 41}, 208--248.
* ↑ Murray, F. J. and von Neumann, J. (1943). On rings of operators IV. Annals of Mathematics , {\mathbf 44}, 716--808.
* ↑ Nahm, W. (1988). Lie group exponents and $SU(2)$ current algebras. Communications in Mathematical Physics , {\mathbf 118}, 171--176.
* ↑ Nahm, W. (1991). A proof of modular invariance. International Journal of Modern Physics , {\mathbf 6}, 2837--2845.
* ↑ Nakanishi, T. and Tsuchiya, A. (1992). Level-rank duality of $WZW$ models in conformal field theory. Communications in Mathematical Physics , {\mathbf 144}, 351--372.
* ↑ von Neumann, J. (1935). Charakterisierung des Spektrums eines Integral Operators. Act. Sci. et Ind. , {\mathbf 229}.
* ↑ von Neumann, J. (1940). On Rings of Operators III. Annals of Mathematics , {\mathbf 41}, 94--161.
* ↑ von Neumann, J. (1961). Collected works vol. III. Rings of Operators. Pergamon Press.
* ↑ Nikshych, D. and Vainerman, L. (2000). A Galois correspondence for $II_{1}$ factors and quantum groupoids. Journal of Functional Analysis , {\mathbf 178}, 113--142.
* ↑ Nill, F. and Wiesbrock, H.-W. (1995). A comment on Jones inclusions with infinite index. Reviews in Mathematical Physics , {\mathbf 7}, 599--630.
* ↑ Ocneanu, A. (1985). Actions of discrete amenable groups on factors , Lecture Notes in Mathematics {\mathbf 1138}, Springer, Berlin.
* ↑ Ocneanu, A. (1988). Quantized group, string algebras and Galois theory for algebras. Operator algebras and applications, Vol. 2 (Warwick, 1987) , (ed. D. E. Evans and M. Takesaki), London Mathematical Society Lecture Note Series Vol. 136, Cambridge University Press, 119--172.
* ↑ Ocneanu, A. (1991). {\em Quantum symmetry, differential geometry of finite graphs and classification of subfactors}, University of Tokyo Seminary Notes 45, (Notes recorded by Kawahigashi, Y.).
* ↑ Ocneanu, A. (1994). Chirality for operator algebras. (recorded by Kawahigashi, Y.) in Subfactors --- Proceedings of the Taniguchi Symposium, Katata --- , (ed. H. Araki, et al.), World Scientific, 39--63.
* ↑ Ocneanu, A. (2000). Paths on Coxeter diagrams: from Platonic solids and singularities to minimal models and subfactors. (Notes recorded by S. Goto), in Lectures on operator theory , (ed. B. V. Rajarama Bhat et al.), The Fields Institute Monographs, Providence, Rhode Island: AMS Publications, 243--323.
* ↑ Ocneanu, A. (2001). Operator algebras, topology and subgroups of quantum symmetry --construction of subgroups of quantum groups--. (recorded by Goto, S. and Sato, N.) in Taniguchi Conference on Mathematics Nara'98 , Advanced Studies in Pure Mathematics {\mathbf 31}, (ed. M. Maruyama and T. Sunada), Mathematical Society of Japan, 235--263.
* ↑ Ocneanu, A. (2002). The classification of subgroups of quantum $SU(N)$. in {\em Quantum Symmetries in Theoretical Physics and Mathematics} (ed. R. Coquereaux et al.), Comtemp. Math. {\mathbf 294}, Amer. Math. Soc., 133--159.
* ↑ Okamoto, S. (1991). Invariants for subfactors arising from Coxeter graphs. Current Topics in Operator Algebras , World Scientific Publishing, 84--103.
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