메뉴 건너뛰기




Volumn 154, Issue 1, 2000, Pages 1-45

Finite quantum groups and Cartan matrices

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0034259899     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1006/aima.1999.1880     Document Type: Article
Times cited : (153)

References (45)
  • 1
    • 0001768267 scopus 로고
    • Representation of quantum groups at a pth root of unity and of semisimple groups in characteristic p: Independence of p
    • Andersen H. H., Jantzen J., Soergel W. Representation of quantum groups at a pth root of unity and of semisimple groups in characteristic p: Independence of p. Astérisque. 220:1994.
    • (1994) Astérisque , vol.220
    • Andersen H., H.1    Jantzen, J.2    Soergel, W.3
  • 7
    • 0031613613 scopus 로고    scopus 로고
    • Hopf (bi-)modules and crossed modules in monoidal categories
    • Bespalov Y., Drabant B. Hopf (bi-)modules and crossed modules in monoidal categories. J. Pure Appl. Algebra. 123:1998;105-129.
    • (1998) J. Pure Appl. Algebra , vol.123 , pp. 105-129
    • Bespalov, Y.1    Drabant, B.2
  • 8
    • 0040914622 scopus 로고    scopus 로고
    • On the number of types of finite-dimensional Hopf algebras
    • Beattie M., Dascalescu S., Grünenfelder L. On the number of types of finite-dimensional Hopf algebras. Invent. Math. 136:1999;1-7.
    • (1999) Invent. Math. , vol.136 , pp. 1-7
    • Beattie, M.1    Dascalescu, S.2    Grünenfelder, L.3
  • 11
    • 22844455397 scopus 로고    scopus 로고
    • Classifying pointed Hopf algebras of dimension 16
    • Caenepeel S., Dascalescu S., Raianu S. Classifying pointed Hopf algebras of dimension 16. Comm. Algebra. 28:2000;541-568.
    • (2000) Comm. Algebra , vol.28 , pp. 541-568
    • Caenepeel, S.1    Dascalescu, S.2    Raianu, S.3
  • 12
    • 0030074875 scopus 로고    scopus 로고
    • The coradical filtration for quantized universal enveloping algebras
    • Chin W., Musson I. The coradical filtration for quantized universal enveloping algebras. J. London Math. Soc. 53:1996;50-67.
    • (1996) J. London Math. Soc. , vol.53 , pp. 50-67
    • Chin, W.1    Musson, I.2
  • 13
    • 0000429580 scopus 로고    scopus 로고
    • Algèbres des chemins quantiques
    • Cibils C., Rosso M. Algèbres des chemins quantiques. Adv. in Math. 125:1997;171-199.
    • (1997) Adv. in Math. , vol.125 , pp. 171-199
    • Cibils, C.1    Rosso, M.2
  • 14
    • 0347802108 scopus 로고    scopus 로고
    • n with large coradical
    • n with large coradical. Comm. Algebra. 27:1999;4821-4826.
    • (1999) Comm. Algebra , vol.27 , pp. 4821-4826
    • Dascalescu, S.1
  • 16
    • 0000843581 scopus 로고
    • On constant, quasi-classical solutions of the quantum Yang-Baxter equation
    • Drinfeld V. G. On constant, quasi-classical solutions of the quantum Yang-Baxter equation. Soviet Math. Dokl. 28:1983;667-671.
    • (1983) Soviet Math. Dokl. , vol.28 , pp. 667-671
    • Drinfeld V., G.1
  • 17
  • 18
    • 0001754777 scopus 로고
    • On quasitriangular quasi-Hopf algebras and a group closely related to Gal(Q, Q)
    • Drinfeld V. G. On quasitriangular quasi-Hopf algebras and a group closely related to Gal(Q, Q). Leningrad Math. J. 2:1991;829-860.
    • (1991) Leningrad Math. J. , vol.2 , pp. 829-860
    • Drinfeld V., G.1
  • 19
    • 0001318754 scopus 로고    scopus 로고
    • On pointed Hopf algebras and Kaplansky's tenth conjecture
    • Gelaki S. On pointed Hopf algebras and Kaplansky's tenth conjecture. J. Algebra. 209:1998;635-657.
    • (1998) J. Algebra , vol.209 , pp. 635-657
    • Gelaki, S.1
  • 20
    • 85037787117 scopus 로고    scopus 로고
    • Pointed Hopf algebras of dimension
    • to appear
    • M. Graña, Pointed Hopf algebras of dimension 32, Comm. Algebra, to appear.
    • Comm. Algebra , vol.32
    • Graña, M.1
  • 21
    • 0001398926 scopus 로고    scopus 로고
    • On Nichols algebras of low dimension
    • to appear
    • M. Graña, On Nichols algebras of low dimension, Contemp. Math, to appear.
    • Contemp. Math
    • Graña, M.1
  • 23
    • 84968491405 scopus 로고    scopus 로고
    • Finite dimensional Hopf algebras arising from quantized universal enveloping algebras
    • G. Lusztig, Finite dimensional Hopf algebras arising from quantized universal enveloping algebras, J. Amer. Math. Soc.3, No. , 257-296.
    • J. Amer. Math. Soc. , vol.3 , Issue.1 , pp. 257-296
    • Lusztig, G.1
  • 24
    • 34249957902 scopus 로고
    • Quantum groups at roots of 1
    • Lusztig G. Quantum groups at roots of 1. Geom. Dedicata. 35:1990;89-114.
    • (1990) Geom. Dedicata , vol.35 , pp. 89-114
    • Lusztig, G.1
  • 26
    • 0002849520 scopus 로고
    • Introduction to quantized enveloping algebras
    • TiraoWallach New Developments in Lie Theory and Their Applications Basel: Birkhäuser
    • Lusztig G. Introduction to quantized enveloping algebras. Tirao, Wallach, . New Developments in Lie Theory and Their Applications. Progr. in Math. 105:1991;49-67 Birkhäuser, Basel.
    • (1991) Progr. in Math. , vol.105 , pp. 49-67
    • Lusztig, G.1
  • 27
    • 0002359613 scopus 로고
    • Crossed products by braided groups and bosonization
    • Majid S. Crossed products by braided groups and bosonization. J. Algebra. 163:1994;165-190.
    • (1994) J. Algebra , vol.163 , pp. 165-190
    • Majid, S.1
  • 30
    • 0003229461 scopus 로고
    • Hopf algebras and their actions on rings
    • Providence: Amer. Math. Soc.
    • Montgomery S. Hopf algebras and their actions on rings. CBMS. 1993;Amer. Math. Soc. Providence.
    • (1993) CBMS
    • Montgomery, S.1
  • 31
    • 0001682244 scopus 로고    scopus 로고
    • Classifying semisemple Hopf algebras
    • Montgomery S. Classifying semisemple Hopf algebras. Contemp. Math. 229:1998;265-279.
    • (1998) Contemp. Math. , vol.229 , pp. 265-279
    • Montgomery, S.1
  • 32
    • 0002192640 scopus 로고
    • Twisting in group algebras of finite groups
    • Movshev M. Twisting in group algebras of finite groups. Funct. Anal. Appl. 27:1994;240-244.
    • (1994) Funct. Anal. Appl. , vol.27 , pp. 240-244
    • Movshev, M.1
  • 33
    • 0039243800 scopus 로고    scopus 로고
    • Some topics on Frobenius-Lusztig kernels, I
    • Müller E. Some topics on Frobenius-Lusztig kernels, I. J. Algebra. 206:1998;624-658.
    • (1998) J. Algebra , vol.206 , pp. 624-658
    • Müller, E.1
  • 34
    • 0040052399 scopus 로고
    • Bialgebras of type one
    • Nichols W. D. Bialgebras of type one. Comm. Algebra. 6:1978;1521-1552.
    • (1978) Comm. Algebra , vol.6 , pp. 1521-1552
    • Nichols W., D.1
  • 35
    • 0043106425 scopus 로고    scopus 로고
    • 0-rings and twisting of finite dimensional semisimple Hopf algebras
    • 0-rings and twisting of finite dimensional semisimple Hopf algebras. Comm. Algebra. 26:1998;321-342.
    • (1998) Comm. Algebra , vol.26 , pp. 321-342
    • Nikshych, D.1
  • 36
    • 46549103268 scopus 로고
    • Hopf algebras with projection
    • Radford D. Hopf algebras with projection. J. Algebra. 92:1985;322-347.
    • (1985) J. Algebra , vol.92 , pp. 322-347
    • Radford, D.1
  • 37
    • 0000834927 scopus 로고
    • Multiparameter quantum groups and twisted quasitriangular Hopf algebras
    • Reshetikhin N. Multiparameter quantum groups and twisted quasitriangular Hopf algebras. Lett. Math. Phys. 20:1990;331-335.
    • (1990) Lett. Math. Phys. , vol.20 , pp. 331-335
    • Reshetikhin, N.1
  • 38
    • 0001880721 scopus 로고
    • Certaines formes bilinéaires sur les groupes quantiques et une conjecture de Schechtman et Varchenko
    • Rosso M. Certaines formes bilinéaires sur les groupes quantiques et une conjecture de Schechtman et Varchenko. C. R. Acad. Sci. Paris. 314:1992;5-8.
    • (1992) C. R. Acad. Sci. Paris , vol.314 , pp. 5-8
    • Rosso, M.1
  • 39
    • 0001344387 scopus 로고
    • Groupes quantiques et algèbres de battage quantiques
    • Rosso M. Groupes quantiques et algèbres de battage quantiques. C. R. Acad. Sci. Paris. 320:1995;145-148.
    • (1995) C. R. Acad. Sci. Paris , vol.320 , pp. 145-148
    • Rosso, M.1
  • 40
    • 0032373319 scopus 로고    scopus 로고
    • Quantum groups and quantum shuffles
    • Rosso M. Quantum groups and quantum shuffles. Invent. Math. 133:1998;399-416.
    • (1998) Invent. Math. , vol.133 , pp. 399-416
    • Rosso, M.1
  • 41
    • 0030269012 scopus 로고    scopus 로고
    • Braided antisymmetrizer as bialgebras homomorphism
    • Rozanski J. Braided antisymmetrizer as bialgebras homomorphism. Rep. Math. Phys. 38:1996;273-277.
    • (1996) Rep. Math. Phys. , vol.38 , pp. 273-277
    • Rozanski, J.1
  • 42
    • 21344446496 scopus 로고    scopus 로고
    • A characterization of the Borel-like subalgebras of quantum enveloping algebras
    • Schauenburg P. A characterization of the Borel-like subalgebras of quantum enveloping algebras. Comm. Algebra. 24:1996;2811-2823.
    • (1996) Comm. Algebra , vol.24 , pp. 2811-2823
    • Schauenburg, P.1
  • 43
    • 85015861081 scopus 로고    scopus 로고
    • Hochschild cohomology and coradical filtration of pointed Hopf algebras
    • Stefan D., van Oystaeyen F. Hochschild cohomology and coradical filtration of pointed Hopf algebras. J. Algebra. 210:1998;125-170.
    • (1998) J. Algebra , vol.210 , pp. 125-170
    • Stefan, D.1    Van Oystaeyen, F.2
  • 45
    • 1542798257 scopus 로고
    • Differential calculus on compact matrix pseudogroups (quantum groups)
    • Woronowicz S. L. Differential calculus on compact matrix pseudogroups (quantum groups). Comm. Math. Phys. 122:1989;125-170.
    • (1989) Comm. Math. Phys. , vol.122 , pp. 125-170
    • Woronowicz S., L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.