Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R.A. Askey, T.H. Koornwinder and W. Schempp, Special Functions: Group Theoretical Aspects and Applications, Mathematics and its Applications (D. Reidel, 1984).
L.C. Biedenharm and J.D. Louck, Angular Momentum in Quantum Physics, Encyclopedia of Mathematics and its Applications 8 (Addison-Wesley, 1981).
L.C. Biedenharm and J.D. Louck, The Racah-Wigner Algebra in Quantum Theory, Encyclopedia of Mathematics and its Applications 9 (Addison-Wesley, 1982).
T. Bröcker and T. tom Dieck, Representations of Compact Lie Groups, Graduate Texts in Math. 98 (Springer-Verlag, Berlin 1985).
P. Cartier, Development recents sur les groupes de tresses. Applications à la topologie et à l'algèbre, Seminaire Bourbaki 42 ie annee, 1989–90, n o 716.
C. Chevalley, Theory of Lie Groups, (Princeton University Press, 1946).
P. Deligne and J.S. Milne, Tannakian categories, Hodge Cocycles Motives and Shimura Varieties, Lecture Notes in Math. 900 (Springer-Verlag, Berlin 1982) 101–228.
S. Doplicher, R. Haag, J.E. Roberts, Local observables and particle statistics II, Comm. Math. Phys. 35 (1974) 49–85.
S. Doplicher and J.E. Roberts, A new duality theory for compact groups, Inventiones Math. 98 (1989) 157–218.
V.G. Drinfel'd, Quantum groups, Proceedings of the International Congress of Mathematicians at Berkeley, California, U.S.A. 1986 (1987) 798–820.
V.G. Drinfel'd, Quasi-Hopf algebras and Knizhnik-Zamolodchikov equations, Acad. Sci. Ukr. (Preprint, ITP-89-43E, 1989)
L.D. Faddeev, N.Yu. Reshetikhin and L.A. Takhtajan, Quantization of Lie algebras and Lie groups, LOMI Preprints (Leningrad 1987); Algebra i Analiz 1:1 (1989, in Russian).
P. Freyd, Abelian Categories, (Harper & Row, New York 1964).
P. Freyd and D. Yetter, Braided compact closed categories with applications to low dimensional topology, Advances in Math. 77 (1989) 156–182.
N. Iwahori and M. Sugiura, A duality theorem for homogeneous compact manifolds of compact Lie groups, Osaka J. Math. 3 (1966) 139–153.
M. Jimbo, A q-difference analog of U(g) and the Yang-Baxter equation, Lett. Math. Phys.10 (1985) 63–69.
V. Jones, A polynomial invariant for knots via von Neumann algebras, Bulletin American Math. Soc. 12 (1985) 103–111.
V. Jones, Index for subfactors, Inventiones Math. 72 (1983) 1–25.
A. Joyal and R. Street, Braided monoidal categories, Macquarie Math. Reports #850067(Dec. 1985); Revised #860081 (Nov. 1986).
A. Joyal and R. Street, The geometry of tensor calculus I, Advances in Math. (to appear).
A. Joyal and R. Street, Braided tensor categories, Advances in Math. (to appear).
A. Joyal and R. Street, Tortile Yang-Baxter operators in tensor categories, J. Pure Appl. Algebra 71 (1991) 43–51.
G.M. Kelly, On clubs and doctrines, Category Seminar Sydney 1972–73, Lecture Notes in Math. 420 (Springer-Verlag, Berlin 1974) 181–256.
S. Kleinman, Motives, Proceedings of the Fifth Nordic Summer School, Oslo 1970 (Wolters-Noordhoff, Holland 1972).
T.H. Koornwinder, Orthogonal polynomials in connection with quantum groups.
M.G. Krein, A principle of duality for a bicompact group and square block algebra, Dokl. Akad. Nauk. SSSR 69 (1949) 725–728.
G. Lewis, Coherence for a closed functor, Coherence in Categories, Lecture Notes in Math. 281 (Springer-Verlag, Berlin 1972) 148–195.
G. Lusztig, Quantum deformations of certain simple modules over enveloping algebras, Advances in Math. 70 (1988) 237–249.
V.V. Lyubashenko, Hopf algebras and vector symmetries, Uspekhi Mat. Nauk. 41 #5 (1986) 185–186.
S. Mac Lane, Categories for the Working Mathematician, Graduate Texts in Math. 5 (Springer-Verlag, Berlin 1971).
Yu.I. Manin, Quantum Groups and Non-Commutative Geometry, Les publications du Centre de Recherches Mathématiques (Université de Montréal, 4e trimestre 1988).
S. Majid, Representations, duals and quantum doubles of monoidal categories, Supl. Rend. Circ. Mat. Palermo (to appear).
S. Majid, Braided groups, Preprint, DAMTP/92-42 (Cambridge 1990).
S. Majid, Tannaka-Krein theorem for quasiHopf algebras and other results, Contemp. Math. (to appear).
B. Pareigis, A non-commutative non-cocommutative Hopf algebra in nature, J. Algebra 70 (1981) 356–374.
R. Penrose, Applications of negative dimensional tensors, Combinatorial Mathematics and its Applications, Edited by D.J.A. Welsh (Academic Press, 1971) 221–244.
P. Podles, Quantum spheres, Lett. Math. Phys. (1987)193–202.
N.Yu. Reshetikhin and V.G. Turaev, Ribbon graphs and their invariants derived from quantum groups, Comm. Math. Phys. 127(1) (1990) 1–26.
M. Rosso, C.R. Acad. Sc. Paris 305, Série I (1987) 587–590.
N. Saavedra Rivano, Catégories Tannakiennes, Lecture Notes in Math. 265 (Springer-Verlag, Berlin 1972).
L. Schwartz, Théorie des Distributions, (Hermann, Paris 1966).
M.C. Shum, Tortile Tensor Categories, PhD Thesis (Macquarie University, November 1989); Macquarie Math. Reports #900047(Apr. 1990).
M.E. Sweedler, Hopf Algebras, Mathematical Lecture Notes Series (Benjamin, 1969).
T Tannaka, Über den Dualitätssatz der nichtkommutativen topologischen Gruppen, Tôhoku Math. J. 45 (1939) 1–12.
V.G. Turaev, The Yang-Baxter equation and invariants of links, Invent. Math. 92 (1988) 527–553.
K.-H. Ulbrich, On Hopf algebras and rigid monoidal categories, Israel J. Math 70 (to appear).
S.L. Woronowicz, Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) groups, Inventiones Math. 93 (1988) 35–76.
D.N. Yetter, Quantum groups and representations of monoidal categories, Math. Proc. Camb. Phil. Soc. (to appear).
D.N. Yetter, Framed tangles and a theorem of Deligne on braided deformations of Tannakian categories, Preprint.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag
About this paper
Cite this paper
Joyal, A., Street, R. (1991). An introduction to Tannaka duality and quantum groups. In: Carboni, A., Pedicchio, M.C., Rosolini, G. (eds) Category Theory. Lecture Notes in Mathematics, vol 1488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084235
Download citation
DOI: https://doi.org/10.1007/BFb0084235
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54706-8
Online ISBN: 978-3-540-46435-8
eBook Packages: Springer Book Archive