메뉴 건너뛰기




Volumn , Issue 581, 2005, Pages 31-69

On braided tensor categories of type BCD

Author keywords

[No Author keywords available]

Indexed keywords


EID: 21644488503     PISSN: 00754102     EISSN: 00754102     Source Type: Journal    
DOI: 10.1515/crll.2005.2005.581.31     Document Type: Article
Times cited : (62)

References (48)
  • 1
    • 0000435046 scopus 로고
    • Tensor products of quantized tilting modules
    • H. H. Andersen, Tensor products of quantized tilting modules, Comm. Math. Phys. 149(1) (1992), 149-159.
    • (1992) Comm. Math. Phys. , vol.149 , Issue.1 , pp. 149-159
    • Andersen, H.H.1
  • 2
    • 0011358712 scopus 로고
    • Quantum groups, invariants of 3-manifolds and semisimple tensor categories
    • Quantum deformations of algebras and their representations (Ramat-Gan 1991/1992; Rehovot 1991/1992)
    • H. H. Andersen, Quantum groups, invariants of 3-manifolds and semisimple tensor categories, in: Quantum deformations of algebras and their representations (Ramat-Gan 1991/1992; Rehovot 1991/1992), Israel Math. Conf. Proc. 7 (1993), 1-12.
    • (1993) Israel Math. Conf. Proc. , vol.7 , pp. 1-12
    • Andersen, H.H.1
  • 3
    • 21844511251 scopus 로고
    • Fusion categories arising from semisimple Lie algebras
    • H. H. Andersen and J. Paradowski, Fusion categories arising from semisimple Lie algebras, Comm. Math. Phys. 169(3) (1995), 563-588.
    • (1995) Comm. Math. Phys. , vol.169 , Issue.3 , pp. 563-588
    • Andersen, H.H.1    Paradowski, J.2
  • 4
    • 0013406573 scopus 로고    scopus 로고
    • Lectures on tensor categories and modular functors
    • American Mathematical Society, Providence, RI
    • B. Bakalov and A. Kirillov, Jr., Lectures on tensor categories and modular functors, Univ. Lect. Ser. 21, American Mathematical Society, Providence, RI (2001).
    • (2001) Univ. Lect. Ser. , vol.21
    • Bakalov, B.1    Kirillov Jr., A.2
  • 5
    • 0003316111 scopus 로고
    • Braids, links, and mapping class groups
    • J. S. Birman, Braids, links, and mapping class groups, Ann. Math. Stud. 82 (1974).
    • (1974) Ann. Math. Stud. , vol.82
    • Birman, J.S.1
  • 6
    • 84966261960 scopus 로고
    • Braids, link polynomials and a new algebra
    • J. S. Birman and H. Wenzl, Braids, link polynomials and a new algebra, Trans. Amer. Math. Soc. 313(1) (1989), 249-273.
    • (1989) Trans. Amer. Math. Soc. , vol.313 , Issue.1 , pp. 249-273
    • Birman, J.S.1    Wenzl, H.2
  • 7
    • 0033633809 scopus 로고    scopus 로고
    • Hecke algebras, modular categories and 3-manifolds quantum invariants
    • C. Blanchet, Hecke algebras, modular categories and 3-manifolds quantum invariants, Topology 39(1) (2000), 193-223.
    • (2000) Topology , vol.39 , Issue.1 , pp. 193-223
    • Blanchet, C.1
  • 8
    • 0000365215 scopus 로고
    • On algebras which are connected with the semisimple continuous groups
    • R. Brauer, On algebras which are connected with the semisimple continuous groups, Ann. Math. 63 (1937), 854-872.
    • (1937) Ann. Math. , vol.63 , pp. 854-872
    • Brauer, R.1
  • 9
    • 84860968838 scopus 로고    scopus 로고
    • Reconstruction des certaines catégories monoidales d'après Kazhdan-Wenzl
    • University of Paris
    • A. Bruguières, Reconstruction des certaines catégories monoidales d'après Kazhdan-Wenzl, Notes for seminar talks, University of Paris.
    • Notes for Seminar Talks
    • Bruguières, A.1
  • 10
    • 0001385854 scopus 로고    scopus 로고
    • La série exceptionnelle de groupes de Lie
    • P. Deligne, La série exceptionnelle de groupes de Lie, C. R. Acad. Sci. Paris Sér. I Math. 322(4) (1996), 321-326.
    • (1996) C. R. Acad. Sci. Paris Sér. I Math. , vol.322 , Issue.4 , pp. 321-326
    • Deligne, P.1
  • 11
    • 0039168742 scopus 로고
    • Almost cocommutative Hopf algebras
    • V. G. Drinfel'd, Almost cocommutative Hopf algebras, Algebra i Analiz 1(2) (1989), 30-46.
    • (1989) Algebra I Analiz , vol.1 , Issue.2 , pp. 30-46
    • Drinfel'd, V.G.1
  • 12
    • 0030304011 scopus 로고    scopus 로고
    • An equivalence of fusion categories
    • M. Finkelberg, An equivalence of fusion categories, Geom. Funct. Anal. 6(2) (1996), 249-267.
    • (1996) Geom. Funct. Anal. , vol.6 , Issue.2 , pp. 249-267
    • Finkelberg, M.1
  • 14
    • 0012335790 scopus 로고
    • Quantum groups, quantum categories and quantum field theory
    • J. Fröhlich and T. Kerler, Quantum groups, quantum categories and quantum field theory, Springer Lect. Notes Math. 1542 (1993).
    • (1993) Springer Lect. Notes Math. , vol.1542
    • Fröhlich, J.1    Kerler, T.2
  • 15
    • 0040323775 scopus 로고
    • A q-difference analogue of U(g) and the Yang-Baxter equation
    • M. Jimbo, A q-difference analogue of U(g) and the Yang-Baxter equation, Lett. Math. Phys. 10(1) (1985), 63-69.
    • (1985) Lett. Math. Phys. , vol.10 , Issue.1 , pp. 63-69
    • Jimbo, M.1
  • 16
    • 43949173985 scopus 로고
    • Braided tensor categories
    • A. Joyal and R Street, Braided tensor categories, Adv. Math. 102(1) (1993), 20-78.
    • (1993) Adv. Math. , vol.102 , Issue.1 , pp. 20-78
    • Joyal, A.1    Street, R.2
  • 19
    • 84966251735 scopus 로고
    • An invariant of regular isotopy
    • L. H. Kauffman, An invariant of regular isotopy, Trans. Amer. Math. Soc. 318(2) (1990), 417-471.
    • (1990) Trans. Amer. Math. Soc. , vol.318 , Issue.2 , pp. 417-471
    • Kauffman, L.H.1
  • 20
    • 84968466254 scopus 로고
    • Tensor structures arising from affine Lie algebras. I, II
    • D. Kazhdan and G. Lusztig, Tensor structures arising from affine Lie algebras. I, II, J. Amer. Math. Soc. 6(4) (1993), 905-947.
    • (1993) J. Amer. Math. Soc. , vol.6 , Issue.4 , pp. 905-947
    • Kazhdan, D.1    Lusztig, G.2
  • 21
    • 84968516064 scopus 로고
    • Tensor structures arising from affine Lie algebras. III
    • D. Kazhdan and G. Lusztig, Tensor structures arising from affine Lie algebras. III, J. Amer. Math. Soc. 7(2) (1994), 335-381.
    • (1994) J. Amer. Math. Soc. , vol.7 , Issue.2 , pp. 335-381
    • Kazhdan, D.1    Lusztig, G.2
  • 22
    • 84968469508 scopus 로고
    • Tensor structures arising from affine Lie algebras. IV
    • D. Kazhdan and G. Lusztig, Tensor structures arising from affine Lie algebras. IV, J. Amer. Math. Soc. 7(2) (1994), 383-453.
    • (1994) J. Amer. Math. Soc. , vol.7 , Issue.2 , pp. 383-453
    • Kazhdan, D.1    Lusztig, G.2
  • 23
    • 0001404104 scopus 로고
    • Reconstructing monoidal categories
    • I. M. Gel' fand Seminar
    • D. Kazhdan and H. Wenzl, Reconstructing monoidal categories, in: I. M. Gel' fand Seminar, Adv. Soviet Math. 16 (1993), 111-136.
    • (1993) Adv. Soviet Math. , vol.16 , pp. 111-136
    • Kazhdan, D.1    Wenzl, H.2
  • 24
    • 0041112898 scopus 로고    scopus 로고
    • On an inner product in modular tensor categories
    • A. A. Kirillov, Jr., On an inner product in modular tensor categories, J. Amer. Math. Soc. 9(4) (1996), 1135-1169.
    • (1996) J. Amer. Math. Soc. , vol.9 , Issue.4 , pp. 1135-1169
    • Kirillov Jr., A.A.1
  • 25
    • 0031568137 scopus 로고    scopus 로고
    • A ribbon Hopf algebra approach to the irreducible representations of centralizer algebras: The Brauer, Birman-Wenzl, and type a Iwahori-Hecke algebras
    • R. Leduc and A. Ram, A ribbon Hopf algebra approach to the irreducible representations of centralizer algebras: the Brauer, Birman-Wenzl, and type A Iwahori-Hecke algebras, Adv. Math. 125(1) (1997), 1-94.
    • (1997) Adv. Math. , vol.125 , Issue.1 , pp. 1-94
    • Leduc, R.1    Ram, A.2
  • 26
    • 0003361511 scopus 로고
    • Introduction to quantum groups
    • G. Lusztig, Introduction to quantum groups, Progr. Math. 110 (1993).
    • (1993) Progr. Math. , vol.110
    • Lusztig, G.1
  • 28
    • 0346763470 scopus 로고
    • Classical and quantum conformal field theory
    • G. Moore and N. Seiberg, Classical and quantum conformal field theory, Comm. Math. Phys. 123(2) (1989), 177-254.
    • (1989) Comm. Math. Phys. , vol.123 , Issue.2 , pp. 177-254
    • Moore, G.1    Seiberg, N.2
  • 30
    • 84972577256 scopus 로고
    • The Kauffman polynomial of links and representation theory
    • J. Murakami, The Kauffman polynomial of links and representation theory, Osaka J. Math. 24(4) (1987), 745-758.
    • (1987) Osaka J. Math. , vol.24 , Issue.4 , pp. 745-758
    • Murakami, J.1
  • 31
    • 0037101523 scopus 로고    scopus 로고
    • Q-centralizer algebras for spin groups
    • R. C. Orellana and H. G. Wenzl, q-centralizer algebras for spin groups, J. Algebra 253 (2) (2002), 237-275.
    • (2002) J. Algebra , vol.253 , Issue.2 , pp. 237-275
    • Orellana, R.C.1    Wenzl, H.G.2
  • 32
    • 38249012379 scopus 로고
    • Matrix units for centralizer algebras
    • A. Ram and H. Wenzl, Matrix units for centralizer algebras, J. Algebra 145(2) (1992), 378-395.
    • (1992) J. Algebra , vol.145 , Issue.2 , pp. 378-395
    • Ram, A.1    Wenzl, H.2
  • 34
    • 1242319001 scopus 로고
    • Deformation cohomology for bialgebras and quasi-bialgebras
    • Deformation theory and quantum groups with applications to mathematical physics (Amherst, MA, 1990)
    • S. Shnider, Deformation cohomology for bialgebras and quasi-bialgebras, in: Deformation theory and quantum groups with applications to mathematical physics (Amherst, MA, 1990), Contemp. Math. 134 (1992), 259-296.
    • (1992) Contemp. Math. , vol.134 , pp. 259-296
    • Shnider, S.1
  • 35
    • 0040431219 scopus 로고    scopus 로고
    • Representations of the braid group 53 and of sl(2,z)
    • I. Tuba and H. Wenzl, Representations of the braid group 53 and of sl(2,z), Pacific J. Math. 197(2) (2001), 491-510.
    • (2001) Pacific J. Math. , vol.197 , Issue.2 , pp. 491-510
    • Tuba, I.1    Wenzl, H.2
  • 36
    • 0040600533 scopus 로고    scopus 로고
    • Semisimple and modular categories from link invariants
    • V. Turaev and H. Wenzl, Semisimple and modular categories from link invariants, Math. Ann. 309(3) (1997), 411-461.
    • (1997) Math. Ann. , vol.309 , Issue.3 , pp. 411-461
    • Turaev, V.1    Wenzl, H.2
  • 37
    • 0003252570 scopus 로고
    • Quantum invariants of knots and 3-manifolds
    • V. G. Turaev, Quantum invariants of knots and 3-manifolds, de Gruyter Stud. Math. 18 (1994).
    • (1994) De Gruyter Stud. Math. , vol.18
    • Turaev, V.G.1
  • 38
    • 45549111952 scopus 로고
    • Fusion rules and modular transformations in 2D conformal field theory
    • E. Verlinde, Fusion rules and modular transformations in 2D conformal field theory, Nuclear Phys. B 300(3) (1988), 360-376.
    • (1988) Nuclear Phys. B , vol.300 , Issue.3 , pp. 360-376
    • Verlinde, E.1
  • 40
    • 0032344404 scopus 로고    scopus 로고
    • Operator algebras and conformal field theory. III, Fusion of positive energy representations of LSU(W) using bounded operators
    • A. Wassermann, Operator algebras and conformal field theory. III, Fusion of positive energy representations of LSU(W) using bounded operators, Invent. Math. 133(3) (1998), 467-538.
    • (1998) Invent. Math. , vol.133 , Issue.3 , pp. 467-538
    • Wassermann, A.1
  • 41
    • 34250096712 scopus 로고
    • Hecke algebras of type an and subfactors
    • H. Wenzl, Hecke algebras of type An and subfactors, Invent. Math. 92(2) (1988), 349-383.
    • (1988) Invent. Math. , vol.92 , Issue.2 , pp. 349-383
    • Wenzl, H.1
  • 42
    • 0001346949 scopus 로고
    • On the structure of Brauer's centralizer algebras
    • H. Wenzl, On the structure of Brauer's centralizer algebras, Ann. Math. (2) 128(1) (1988), 173-193.
    • (1988) Ann. Math. (2) , vol.128 , Issue.1 , pp. 173-193
    • Wenzl, H.1
  • 43
    • 7244225268 scopus 로고
    • Quantum groups and subfactors of type B, C, and D
    • H. Wenzl, Quantum groups and subfactors of type B, C, and D, Comm. Math. Phys. 133(2) (1990), 383-432.
    • (1990) Comm. Math. Phys. , vol.133 , Issue.2 , pp. 383-432
    • Wenzl, H.1
  • 44
    • 0032396086 scopus 로고    scopus 로고
    • C* tensor categories from quantum groups
    • H. Wenzl, C* tensor categories from quantum groups, J. Amer. Math. Soc. 11(2) (1998), 261-282.
    • (1998) J. Amer. Math. Soc. , vol.11 , Issue.2 , pp. 261-282
    • Wenzl, H.1
  • 45
    • 21644465467 scopus 로고    scopus 로고
    • Tensor categories and braid representations
    • Quantum groups and Lie theory (Durham 1999)
    • H. Wenzl, Tensor categories and braid representations, in: Quantum groups and Lie theory (Durham 1999), London Math. Soc. Lect. Note Ser. 290 (2001), 216-234.
    • (2001) London Math. Soc. Lect. Note Ser. , vol.290 , pp. 216-234
    • Wenzl, H.1
  • 46
    • 21644457459 scopus 로고    scopus 로고
    • Princeton University Press, Princeton, NJ, their invariants and representations, Fifteenth printing, Princeton Paperbacks
    • H. Weyl, The classical groups, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 1997, their invariants and representations, Fifteenth printing, Princeton Paperbacks.
    • (1997) The Classical Groups, Princeton Landmarks in Mathematics
    • Weyl, H.1
  • 47
    • 14644388676 scopus 로고
    • Quantum field theory and the Jones polynomial
    • E. Wirten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121(3) (1989), 351-399.
    • (1989) Comm. Math. Phys. , vol.121 , Issue.3 , pp. 351-399
    • Wirten, E.1
  • 48
    • 0010104071 scopus 로고
    • Markov algebras
    • Braids (Santa Cruz, CA, 1986)
    • D. N. Yetter, Markov algebras, in: Braids (Santa Cruz, CA, 1986), Contemp. Math. 78 (1988), 705-730.
    • (1988) Contemp. Math. , vol.78 , pp. 705-730
    • Yetter, D.N.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.