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

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\begin{thebibliography} {299} \bibitem{KSW} 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. {\em Advances in Mathematics}, {\bf 195}, 165-179. \bibitem{KLu} Kazhdan, V. and Lusztig, G. (1994). Tensor structures arising from affine Lie algebras. {\em IV, Journal of the American Mathematical Society}, {\bf 7}, 383--453.

\bibitem{Ki} Kirby, R. (1978). A calculus of farmed links in $S^3$. {\em Inventiones Mathematicae}, {\bf 45}, 35--56.

\bibitem{KM} Kirby, R. and Melvin, P. (1990). On the $3$-manifold invariants of Witten and Reshetikhin--Turaev. {\em Inventiones Mathematicae}, {\bf 105}, 473--545.

\bibitem{KO} Kirillov, A. Jr. and Ostrik, V. (2002). On $q$-analog of McKay correspondence and ADE classification of $sl^{(2)}$ conformal field theories. {\em Advances in Mathematics}, {\bf 171}, 183--227. math.QA/0101219.

\bibitem{KiR} Kirillov, A. N. and Reshetikhin, N. Yu. (1988). Representations of the algebra $U_q(sl_2)$, $q$-orthogonal polynomials and invariants for links. {\em Infinite dimensional Lie algebras and groups}, (Ka\v c, V. G., ed.), Advanced Series in Mathematical Physics, vol. 7, 285--339.

\bibitem{KZ} Knizhnik, V. and Zamolodchikov, A. (1984). Current algebra and Weiss-Zumino models in two dimensions. {\em Nuclear Physics B}, {\bf 247}, 83--103.

\bibitem{KS1} Kodiyalam, V. and Sunder, V. S. (2001). Spectra of principal graphs. {\em International Journal of Mathematics}, {\bf 12}, 203--210.

\bibitem{KS2} Kodiyalam, V. and Sunder, V. S. (2001). Flatness and fusion coefficients. {\em Pacific Journal of Mathematics}, {\bf 201}, 177--204.

\bibitem{KS3} Kodiyalam, V. and Sunder, V. S. (2001). Topological quantum field theories from subfactors. Chapman \& Hall/CRC, Research Notes in Mathematics, {\bf 423}.

\bibitem{Kn} Kohno, T. (1987). Monodromy representations of braid groups and Yang--Baxter equations. {\em Annales de l'Institut Fourier, Grenoble}, {\bf 37,4}, 139--160.

\bibitem{Kn1} Kohno, T. (1992). Topological invariants for $3$-manifolds using representations of mapping class groups I. {\em Topology}, {\bf 31}, 203--230.

\bibitem{Kn2} Kohno, T. (1992). Three-manifold invariants derived from conformal field theory and projective representations of modular groups. {\em International Journal of Modern Physics}, {\bf 6}, 1795--1805.

\bibitem{Ko1} Kosaki, H. (1986). Extension of Jones' theory on index to arbitrary factors. {\em Journal of Functional Analysis}, {\bf 66}, 123--140.

\bibitem{Ko2} Kosaki, H. (1989). Characterization of crossed product (properly infinite case). {\em Pacific Journal of Mathematics}, {\bf 137}, 159--167.

\bibitem{Ko3} 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.

\bibitem{Ko4} Kosaki, H. (1993). Automorphisms in the irreducible decompositions of sectors. {\em Quantum and non-commutative analysis}, (ed. H. Araki et al.), Kluwer Academic, 305--316.

\bibitem{Ko5} Kosaki, H. (1994). AFD factor of type III$_0$ with many isomorphic index 3 subfactors. {\em Journal of Operator Theory}, {\bf 32}, 17--29.

\bibitem{Ko6} Kosaki, H. (1994). Some remarks on automorphisms for inclusions of type III factors. in {\em Subfactors --- Proceedings of the Taniguchi Symposium, Katata ---}, (ed. H. Araki, et al.), World Scientific, 153--171.

\bibitem{Ko7} Kosaki, H. (1996). Sector theory and automorphisms for factor-subfactor pairs. {\em Journal of the Mathematical Society of Japan}, {\bf 48}, 427--454.

\bibitem{KLoi} Kosaki, H. and Loi, P. H. (1995). A remark on non-splitting inclusions of type III$_1$ factors. {\em International Journal of Mathematics}, {\bf 6}, 581--586.

\bibitem{KL} Kosaki, H. and Longo, R. (1992). A remark on the minimal index of subfactors. {\em Journal of Functional Analysis}, {\bf 107}, 458--470.

\bibitem{KMY} Kosaki, H., Munemasa, A. and Yamagami, S. (1997). On fusion algebras associated to finite group actions. {\em Pacific Journal of Mathematics}, {bf 177}, 269--290.

\bibitem{KY} Kosaki, H. and Yamagami, S. (1992). Irreducible bimodules associated with crossed product algebras. {\em International Journal of Mathematics}, {\bf 3}, 661--676.

\bibitem{Ks} K\"oster, S. (2002). Conformal transformations as observables. {\em Letters in Mathematical Physics}, {\bf 61}, 187--198.

\bibitem{Ks2} K\"oster, S. (preprint 2003). Absence of stress energy tensor in CFT$_2$ models. math-ph/0303053.

\bibitem{Ks3} K\"oster, S. (2004). Local nature of coset models. {\em Reviews in Mathematical Physics}, {\bf 16}, 353--382. math-ph/0303054.

\bibitem{Ks4} K\"oster, S. (preprint 2003). Structure of coset models. math-ph/0308031.

\bibitem{Kv} Kostov, I. (1988). Free field presentation of the $A_n$ coset models on the torus. {\em Nuclear Physics B}, {\bf 300}, 559--587.

\bibitem{KW} Kramers, H. A. and Wannier, G. H. (1941). Statistics of the two dimensional ferromagnet part 1. {\em Physical Review}, {\bf 60}, 252--262.

\bibitem{Ku} Kuik, R. (1986). On the $q$-state Potts model by means of non-commutative algebras. Ph.D. Thesis Groningen.

\bibitem{KuR} Kulish, P. and Reshetikhin, N. (1983). Quantum linear problem for the sine-Gordon equation and higher representations. {\em Journal of Soviet Mathematics}, {\bf 23}, 2435--2441.

\bibitem{KAW} Kuniba, A., Akutsu, Y. and Wadati, M. (1986). Virasoro algebra, von Neumann algebra and critical eight vertex SOS model. {\em Journal of Physics Society of Japan}, {\bf 55}, 3285--3288.

\bibitem{La1} Landau, Z. (2001). Fuss-Catalan algebras and chains of intermediate subfactors. {\em Pacific Journal of Mathematics}, {\bf 197}, 325--367.

\bibitem{La2} Landau, Z. (2002). Exchange relation planar algebras. {\em Journal of Functional Analysis}, {\bf 195}, 71--88.

\bibitem{Lic} Lickorish, W. (1988). Polynomials for links. {\em Bulletin of the American Mathematical Society}, {\bf 20}, 558--588.

\bibitem{Loi1} Loi, P. H. (1988). On the theory of index and type III factors. Thesis, Pennsylvania State University.

\bibitem{Loi2} Loi, P. H. (1996). On automorphisms of subfactors. {\em Journal of Functional Analysis}, {\bf 141}, 275--293.

\bibitem{Loi3} Loi, P. H. (1994). On the derived tower of certain inclusions of type III$_\lambda$ factors of index 4. {\em Pacific Journal of Mathematics}, {\bf 165}, 321--345.

\bibitem{Loi4} Loi, P. H. (1994). Remarks on automorphisms of subfactors. {\em Proceedings of the American Mathematical Society}, {\bf 121}, 523--531.

\bibitem{Loi5} Loi, P. H. (1997). Periodic and strongly free automorphisms on inclusions of type III$_\lambda$ factors. {\em International Journal of Mathematics}, {\bf 8}, 83--96.

\bibitem{Loi6} Loi, P. H. (1998). A structural result of irreducible inclusions of type III$_\lambda$ factors. {\em Proceedings of the American Mathematical Society}, {\bf 126}, 2651--2662.

\bibitem{Loi7} Loi, P. H. (1998). Commuting squares and the classification of finite depth inclusions of AFD type III$_\lambda$ factors, $\lambda\in(0,1)$. {\em Publications of the RIMS, Kyoto University}, {\bf 34}, 115--122.

\bibitem{Lo} Loke, T. (1994). Operator algebras and conformal field theory of the discrete series representations of Diff$(S^1)$. {\em Thesis, University of Cambridge}.

\bibitem{Ln1} Longo, R. (1978) A simple proof of the existence of modular automorphisms in approximately finite dimensional von Neumann algebras. {\em Pacific Journal of Mathematics}, {\bf 75}, 199--205.

\bibitem{Ln2} Longo, R. (1979). Automatic relative boundedness of derivations in $C^*$-algebras. {\em Journal of Functional Analysis}, {\bf 34}, 21--28.

\bibitem{Ln3} Longo, R. (1984). Solution of the factorial Stone-Weierstrass conjecture. An application of the theory of standard split $W^*$-inclusions. {\em Inventiones Mathematicae}, {\bf 76}, 145--155.

\bibitem{Ln4} Longo, R. (1987). Simple injective subfactors. {\em Advances in Mathematics}, {\bf 63}, 152--171.

\bibitem{Ln5} Longo, R. (1989). Index of subfactors and statistics of quantum fields, I. {\em Communications in Mathematical Physics}, {\bf 126}, 217--247.

\bibitem{Ln6} Longo, R. (1990). Index of subfactors and statistics of quantum fields II. {\em Communications in Mathematical Physics}, {\bf 130}, 285--309.

\bibitem{Ln7} Longo, R. (1992). Minimal index and braided subfactors. {\em Journal of Functional Analysis}, {\bf 109}, 98--112.

\bibitem{Ln8} Longo, R. (1994). A duality for Hopf algebras and for subfactors I. {\em Communications in Mathematical Physics}, {\bf 159}, 133--150.

\bibitem{Ln9} Longo, R. (1994). Problems on von Neumann algebras suggested by quantum field theory. in {\em Subfactors --- Proceedings of the Taniguchi Symposium, Katata ---}, (ed. H. Araki, et al.), World Scientific, 233--241.

\bibitem{Ln10} Longo, R. (1997). An analogue of the Kac-Wakimoto formula and black hole conditional entropy. {\em Communications in Mathematical Physics}, {\bf 186}, 451--479.

\bibitem{Ln11} Longo, R. (1999). On the spin-statistics relation for topological charges. in {\em Operator Algebras and Quantum Field Theory} (ed. S. Doplicher, et al.), International Press, 661--669.

\bibitem{Ln12} Longo, R. (2001). Notes for a quantum index theorem. {\em Communications in Mathematical Physics}, {\bf 222}, 45--96.

\bibitem{Ln13} Longo, R. (2003). Conformal subnets and intermediate subfactors. {\em Communications in Mathematical Physics}, {\bf 237}, 7--30. math.OA/0102196.

\bibitem{LRe} Longo, R. and Rehren, K.-H. (1995). Nets of subfactors. {\em Reviews in Mathematical Physics}, {\bf 7}, 567--597.

\bibitem{LRe2} Longo, R. and Rehren, K.-H. (2004). Local fields in boundary CFT. {\em Reviews in Mathematical Physics}, {\bf 16}, 909--960. math-ph/0405067.

\bibitem{LRe3} Longo, R. and Rehren, K.-H. (preprint 2007). How to remove the boundary. arXiv:0712.2140.

\bibitem{LRo} Longo, R. and Roberts, J. E. (1997). A theory of dimension. {\em $K$-theory}, {\bf 11}, 103--159.

\bibitem{LX} Longo, R. and Xu, F. (2004). Topological sectors and a dichotomy in conformal field theory. {\em Communications in Mathematical Physics}, {\bf 251}, 321--364. math.OA/0309366.

\bibitem{Mar} Markov, A. (1935). \"Uber de freie Aquivalenz geschlossener Z\"opfe. {\em Rossiiskaya Akademiya Nauk, Matematicheskii Sbornik}, {\bf 1}, 73--78.

\bibitem{Masuda} Masuda, T. (1997). An analogue of Longo's canonical endomorphism for bimodule theory and its application to asymptotic inclusions. {\em International Journal of Mathematics}, {\bf 8}, 249--265.

\bibitem{Masuda2} Masuda, T. (1999). Classification of actions of discrete amenable groups on strongly amenable subfactors of type $III_\lambda$. {\em Proceedings of the American Mathematical Society}, {\bf 127}, 2053--2057.

\bibitem{Masuda3} Masuda, T. (1999). Classification of strongly free actions of discrete amenable groups on strongly amenable subfactors of type $III_0$. {\em Pacific Journal of Mathematics}, {\bf 191}, 347--357.

\bibitem{Masuda4} Masuda, T. (2000). Generalization of Longo-Rehren construction to subfactors of infinite depth and amenability of fusion algebras. {\em Journal of Functional Analysis}, {\bf 171}, 53--77.

\bibitem{Masuda5} Masuda, T. (2001). Extension of automorphisms of a subfactor to the symmetric enveloping algebra. {\em International Journal of Mathematics}, {\bf 12}, 637--659.

\bibitem{Masuda6} Masuda, T. (in press). Classification of approximately inner actions of discrete amenable groups on strongly amenable subfactors. {\em International Journal of Mathematics},

\bibitem{Masuda7} Masuda, T. (2003).Notes on group actions on subfactors. {\em Journal of the Mathematical Society of Japan}, {\bf 55}, 1--11.

\bibitem{Masuda8} Masuda, T. (2003). On non-strongly free automorphisms of subfactors of type III$_0$. {\em Canadian Mathematical Bulletin}, {\bf 46}, 419--428.

\bibitem{Masuda9} Masuda, T. (2005). An analogue of Connes-Haagerup approach to classification of subfactors of type $III_1$. {\em Journal of the Mathematical Society of Japan}, {\bf 57}, 959--1001.

\bibitem{MWu} McCoy, B. and Wu, T. (1972). The two dimensional Ising model. {\em Harvard University Press, Cambridge, Massachusetts}, {\bf 40}.

\bibitem{McD1} McDuff, D. (1969). Uncountably many $II_1$ factors. {\em Annals of Mathematics}, {\bf 90}, 372--377.

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\bibitem{MS} Moore, G. and Seiberg, N. (1989). Classical and quantum conformal field theory. {\em Communications in Mathematical Physics}, {\bf 123}, 177--254.

\bibitem{MS1} Moore, G. and Seiberg, N. (1989). Naturality in conformal field theory. {\em Nuclear Physics B}, {\bf 313}, 16--40.

\bibitem{Mg1} M\"uger, M. (1998). Superselection structure of massive quantum field theories in $1+1$ dimensions. {\em Reviews in Mathematical Physics}, {\bf 10}, 1147--1170.

\bibitem{Mg2} M\"uger, M. (1999). On soliton automorphisms in massive and conformal theories. {\em Reviews in Mathematical Physics}, {\bf 11}, 337--359.

\bibitem{Mg3} M\"uger, M. (1999). On charged fields with group symmetry and degeneracies of Verlinde's matrix $S$. {\em Annales de l'Institut Henri Poincar\'e. Physique Th\'eorique}, {\bf 71}, 359--394.

\bibitem{Mg4} M\"uger, M. (2000). Galois theory for braided tensor categories and the modular closure. {\em Advances in Mathematics}, {\bf 150}, 151--201.

\bibitem{Mg5} M\"uger, M. (2001). Conformal field theory and Doplicher-Roberts reconstruction. in {\em Mathematical Physics in Mathematics and Physics} (ed. R. Longo), The Fields Institute Communications {\bf 30}, Providence, Rhode Island: AMS Publications, 297--319. math-ph/0008027.

\bibitem{Mg6} M\"uger, M. (2003). From subfactors to categories and topology I. Frobenius algebras in and Morita equivalence of tensor categories. {\em Journal of Pure and Applied Algebra}, {\bf 180}, 81--157. math.CT/0111204.

\bibitem{Mg7} M\"uger, M. (2003). From subfactors to categories and topology II. The quantum double of subfactors and categories. {\em Journal of Pure and Applied Algebra}, {\bf 180}, 159--219. math.CT/0111205.

\bibitem{Mg8} M\"uger, M. (in press). On the structure of modular categories. {\em Proceedings of the London Mathematical Society}. math.CT/0201017.

\bibitem{Mg9} M\"uger, M. (preprint 2002). Galois extensions of braided tensor categories and braided crossed G-categories. math.CT/0209093.

\bibitem{Mg10} M\"uger, M. (2005). Conformal orbifold theories and braided crossed G-categories {\em Communications in Mathematical Physics}, {\bf 260}, 727--762. math.QA/0403322.

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