journal article Jun 01, 1990

Index of subfactors and statistics of quantum fields

View at Publisher Save 10.1007/bf02473354
Topics

No keywords indexed for this article. Browse by subject →

References
36
[1]
Combes, F., Delaroche, C.: Groupe modulaire d'une esperance conditionnelle dans une algèbre de un Neumann, Bull. Soc. Math. France103, 385–426 (1975) 10.24033/bsmf.1808
[2]
Connes, A.: Periodic automorphisms of the hyperfinite factor of type II. Acta Sci. Math.39, 39–66 (1977)
[3]
Connes, A.: On the spatial theory of von Neumann algebras. J. Funct. Anal.35, 153–164 (1980) 10.1016/0022-1236(80)90002-6
[4]
Connes, A.: unpublished; see Connes, A., Jones, V. R. F.: Property T for von Neumann algebras. Bull. Lond. Math. Soc.17, 57 (1985); Popa, S.: Correspondences, preprint; Sauvageot, J. L.: Sur le produit tensoriel relatif de'espaces de Hilbert. J. Oper. Th.9, 237–252 (1983) 10.1112/blms/17.1.57
[5]
Doplicher, S., Haag, R., Roberts, J. E.: Local observables and particle statistics. I, Commun. Math. Phys.35, (1971), 199–230; II, Commun. Math. Phys.35, 49–85 (1974) 10.1007/bf01877742
[6]
Fredenhagen, K., Rehren, K. H., Schroer, B.: Superselectrion sectors with braid group statistics and exchange algebras, I: General theory. Commun. Math. Phys.125, 201–226 (1989) 10.1007/bf01217906
[7]
Freyd, P., Yetter, D., Hoste, J., Lickorish, W., Millet, K., Ocneanu, A.: A new polynomial invariant for knots and links. Bull. AMS12, 103–111 (1985) 10.1090/s0273-0979-1985-15361-3
[8]
Fröhlich, J.: Statistics of fields, the Yong—Baxter equation, and the theory of links and knots. In: Nonperturbative quantum field theory, New York: Plenum Press (1988); Rehren, K. H., Schroer, B.: Einstein causality and Artin braids. Nucl. Phys.312, 3 (1989) Tsuchiya, A., Kanie, Y.: Vertex operators in conformal field theory on ℙ1 and monodromy representations of braid groups. Adv. Studies Pure Math.16, 297–372 (1988)
[9]
Haagerup, U.: Operator valued weights in von Neumann algebras. I, II, J. Funct. Anal.32, 175–206 (1979),33, 339–361 (1979) 10.1016/0022-1236(79)90053-3
[10]
Kosaki, H., Longo, R.: work in progress
[11]
Kosaki, H.: Extension of Jones theory on index to arbitrary factors. J. Funct. Anal.66, 123–140 (1986) 10.1016/0022-1236(86)90085-6
[12]
Index for subfactors

V. F. R. Jones

Inventiones mathematicae 1983 10.1007/bf01389127
[13]
Jones, V. R. F.: Hecke algebra representations of braid groups and link polynomials. Ann. Math.126, 335–388 (1987) 10.2307/1971403
[14]
Jones, V. R. F.: Braid groups, Hecke algebras and type II1, factors. In: Geometric Methods in Operator Algebras. Proc. US-Japan seminar 242–273
[15]
Loi, P. H.: On the theory of index and type III factors. Penn. State Univ. Thesis (1988)
[16]
Longo, R.: Solution of the factorial Stone-Weierstrass conjecture. Invent. Math.76, 145–155 (1984) 10.1007/bf01388497
[17]
Longo, R.: Simple injective subfactors. Adv. Math.63, 152–171 (1987) 10.1016/0001-8708(87)90051-x
[18]
Longo, R.: Index of subfactors and statistics of quantum fields. I. Commun. Math. Phys.126, 217–247 (1989) 10.1007/bf02125124
[19]
Longo, R.: Inclusions of von Neumann algebras and quantum fied theory. In IXth International Congress on Mathematical Physics. Simon, B., Truman, A., Davis, I. M. (eds.), Swansea, July 1988, Bristol, New York: Adam Hilger
[20]
Ocneanu, A.: Quantized groups, string algebras and Galois theory for algebras. Lond. Math. Soc., Lecture Notes vol.136. Evans, D., Takesaki., M. (eds.) pp.119–172 (1989)
[21]
Pimsner, M., Popa, S.: Entropy and index for subfactors. Ann. Sci. Ec. Norm. Sup.19, 57–106 (1986) 10.24033/asens.1504
[22]
Powers, R. T.: An index theory for semigroups of endomorphisms of B(H) and type II1 factors. Can. J. Math40, 86–114 (1988) 10.4153/cjm-1988-004-3
[23]
Temperley, H., Lieb, E.: Relation between the percolation and colouring problem. Proc. R. Soc. (London) 251–280 (1971) 10.1098/rspa.1971.0067
[24]
Wenzl, H.: Hecke algebras of type A n and subfactors. Invent. Math.92, 349–383 (1988) 10.1007/bf01404457
[25]
Witten, E.: Quantum Field Theory and the Jones polynomial. Commun. Math. Phys.121, 351–399 (1989) 10.1007/bf01217730
[26]
Birman, J. S., Wenzl, H.: Braids, link polynomials and a new algebra. Trans. AMS313, 249–273 (1989) 10.1090/s0002-9947-1989-0992598-x
[27]
Wenzl, H.: Quantum groups and subfactors of type B, C and D, preprint
[28]
Murakami, J.: The Kauffman polynomial of links and representation theory. Osaka J. Math.24, 745–758 (1987)
[29]
Kauffman, L. H.: An invaraint of regular isotopy. Trans. AMS (to appear);
[30]
Gepner, D., Witten, E.: String theory on group manifolds. Nucl. Phys. B278, 493–549 (1986) 10.1016/0550-3213(86)90051-9
[31]
Verlinde, E.: Fusion rules and modular transformations in 2D conformal field theory. Nucl. Phys.B300, 360 (1988) 10.1016/0550-3213(88)90603-7
[32]
Frohlich, J., King, C.: Two-dimensional conformal field theory and three-dimensional topology. Preprint
[33]
Wasserman, A. J.: Coactions and Yang-Baxter equations for ergodic actions and subfactors. London Math. Soc. Lecture Notes vol. 136. Evans, D., Takesaki, M. (eds.) pp. 173–193, 1988
[34]
The A-D-E classification of minimal andA 1 (1) conformal invariant theories

A. Cappelli, C. Itzykson, J. B. Zuber

Communications in Mathematical Physics 1987 10.1007/bf01221394
[35]
Chode, M.: Entropy for canonical shifts. Preprint
[36]
Reheren, K. H.: Braid group statistics and their superselection structures. Preprint
Metrics
119
Citations
36
References
Details
Published
Jun 01, 1990
Vol/Issue
130(2)
Pages
285-309
License
View
Cite This Article
Roberto Longo (1990). Index of subfactors and statistics of quantum fields. Communications in Mathematical Physics, 130(2), 285-309. https://doi.org/10.1007/bf02473354
Related

You May Also Like

Particle creation by black holes

S. W. Hawking · 1975

10,628 citations

On the generators of quantum dynamical semigroups

G. Lindblad · 1976

6,183 citations

The four laws of black hole mechanics

J. M. Bardeen, B. Carter · 1973

3,127 citations

Non-abelian bosonization in two dimensions

Edward Witten · 1984

1,940 citations

Intermittent transition to turbulence in dissipative dynamical systems

Yves Pomeau, PAUL MANNEVILLE · 1980

1,701 citations