Galois theory for braided tensor categories and the modular closure

Advances in Mathematics

Volumn 150, Issue 2, 2000, Pages 151-201

  Müger, Michael ^a  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0345856521     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1006/aima.1999.1860     Document Type: Article

References (34)

1. Albeverio S., Høegh-Krohn R. Ergodic actions by compact groups on C*-algebras. Math. Z. 174:1980;1-17.
2. Baez J. C. Higher dimensional algebra. II. 2-Hilbert spaces. Adv. Math. 127:1997;125-189.
3. Curtis C. W., Reiner I. Representation Theory of Finite Groups and Associative Algebras. 1962;Wiley, New York.
4. Deligne P., Milne J. S. Tannakian categories. Hodge Cycles, Motives, and Shimura Varieties. Lecture Notes in Math. 900:1982;Springer-Verlag, New York/Berlin. p. 101-228.
5. Deligne P. Catégories Tannakiennes. Grothendieck Festschrift. 1991;Birkhäuser, Basel. p. 111-193.
6. Doplicher S., Roberts J. E. A new duality theory for compact groups. Invent. Math. 98:1989;157-218.
7. Doplicher S., Roberts J. E. Why there is a field algebra with a compact gauge group describing the superselection structure in particle physics. Comm. Math. Phys. 131:1990;51-107.
8. Evans D. E., Kawahigashi Y. Orbifold subfactors from Hecke algebras, I. Comm. Math. Phys. 165:1994;445-484.
9. Fuchs J., Schellekens A. N., Schweigert C. A matrix S for all simple current extensions. Nucl. Phys. B. 473:1996;323-366.
10. Ghez P., Lima R., Roberts J. E. W*-Categories. Pacific J. Math. 120:1985;79-109.
11. Grothendieck A. Revêtements étales et groupe fondamental (SGA 1). Lecture Notes in Math. 224:1972;Springer-Verlag, New York/Berlin.
12. Høegh-Krohn R., Landstad M. B., Størmer E. Compact ergodic groups of automorphisms. Ann. Math. 114:1981;75-86.
13. Janelidze G. The fundamental theorem of Galois theory. Math. USSR Sb. 64:1989;359-374.
14. Joyal A., Street R. Braided tensor categories. Adv. Math. 102:1993;20-78.
15. Karpilovsky G. Projective Representations of Finite Groups. 1985;Dekker, New York.
16. Kastler D. The Algebraic Theory of Superselection Sectors: Introduction and Recent Results. 1990;World Scientific, Singapore.
17. Kastler D., Mebkhout M., Rehren K.-H. Introduction to the algebraic theory of superselection sectors (space-time dimension=2 - strictly localized morphisms). The Algebraic Theory of Superselection Sectors: Introductions and Recent Results. 1990;World Scientific, Singapore.
18. Kerler T., Roberts J. E. Mapping class group actions on quantum doubles. Comm. Math. Phys. 168:1995;353-388.
19. Longo R., Roberts J. E. A theory of dimension. K-Theory. 11:1997;103-159.
20. Mac Lane S. Categories for the Working Mathematician. 1998;Springer-Verlag, New York/Berlin.
21. Müger M. On charged fields with group symmetry and degeneracies of Verlinde's matrix S. Ann. Inst. H. Poincaré Phys. Théor. 71:1999;359-394.
22. M. Müger, On Galois extension of braided tensor categories, mapping class group representations and quantum field theory, in preparation.
23. Rehren K.-H. Braid group statistics and their superselection rules. The Algebraic Theory of Superselection Sectors: Introduction and Recent Results. 1990;World Scientific, Singapore.
24. Rehren K.-H. Markov traes as characters for local algebras. Nucl. Phys. B(Proc. Suppl.). 18:1990;259-268.
25. J. E. Roberts, The reconstruction problem, unpublished manuscript, 1971.
26. Roberts J. E. Lectures on algebraic quantum field theory. The Algebraic Theory of Superselection Sectors: Introduction and Recent Results. 1990;World Scientific, Singapore.
27. J. E. Roberts, and, L. Tuset, On the equality of q-dimension and intrinsic dimension, J. Pure Appl. Alg, in press.
28. Saaveda Rivano N. Catégories Tannakiennes. Lecture Notes in Math. 265:1972;Springer-Verlag, New York/Berlin.
29. Turaev V. G. Quantum Invariants of Knots and 3-Manifolds. 1994;de Gruyter, Berlin/New York.
30. Turaev V. G., Wenzl H. Semisimple and modular categories from link invariants. Math. Ann. 309:1997;411-461.
31. Wassermann A. Ergodic actions of compact groups on operator algebras, I. Ann. Math. 130:1989;411-319.
32. Wenzl H. C*-Tensor categories from quantum groups. J. Amer. Math. Soc. 11:1998;261-282.
33. Xu F. Orbifold construction in subfactors. Comm. Math. Phys. 166:1994;237-253.
34. S. Yamagami, Tensor categories for operator algebraists, unpublished notes, 1998.