메뉴 건너뛰기




Volumn 270, Issue 2, 2003, Pages 670-695

On oriented quantum algebras derived from representations of the quantum double of a finite-dimensional Hopf algebra

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0346899405     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jalgebra.2003.07.006     Document Type: Article
Times cited : (32)

References (27)
  • 1
    • 0003355798 scopus 로고
    • Hopf Algebras
    • Cambridge Univ. Press, Cambridge, UK
    • E. Abe, Hopf Algebras, in: Cambridge Tracts in Math., Vol. 74, Cambridge Univ. Press, Cambridge, UK, 1980.
    • (1980) Cambridge Tracts in Math. , vol.74
    • Abe, E.1
  • 2
    • 0001768267 scopus 로고
    • Representations of quantum groups at a pth root of unity and of semisimple groups in characteristic p: Independence of p
    • H.H. Andersen, J.C. Jantzen, W. Soergel, Representations of quantum groups at a pth root of unity and of semisimple groups in characteristic p: independence of p, Astérisque 220 (1994) 321.
    • (1994) Astérisque , vol.220 , pp. 321
    • Andersen, H.H.1    Jantzen, J.C.2    Soergel, W.3
  • 3
    • 0034259899 scopus 로고    scopus 로고
    • Finite quantum groups and Cartan matrices
    • N. Andruskiewitsch, H.-J. Schneider, Finite quantum groups and Cartan matrices, Adv. Math. 154 (2000) 1-45.
    • (2000) Adv. Math. , vol.154 , pp. 1-45
    • Andruskiewitsch, N.1    Schneider, H.-J.2
  • 4
    • 0036178628 scopus 로고    scopus 로고
    • Finite quantum groups over abelian groups of prime exponent
    • N. Andruskiewitsch, H.-J. Schneider, Finite quantum groups over abelian groups of prime exponent, Ann. Sci. École Norm. Sup. (4) 35 (2002) 1-26.
    • (2002) Ann. Sci. École Norm. Sup. , vol.35 , Issue.4 , pp. 1-26
    • Andruskiewitsch, N.1    Schneider, H.-J.2
  • 6
    • 0034148634 scopus 로고    scopus 로고
    • Irreducible representations of a class of quantum doubles
    • H.-X. Chen, Irreducible representations of a class of quantum doubles, J. Algebra 225 (2000) 391-409.
    • (2000) J. Algebra , vol.225 , pp. 391-409
    • Chen, H.-X.1
  • 7
    • 0000805003 scopus 로고
    • On almost cocommutative Hopf algebras
    • (translation)
    • V.G. Drinfel'd, On almost cocommutative Hopf algebras, Leningrad Math J. 1 (1990) 321-342 (translation).
    • (1990) Leningrad Math J. , vol.1 , pp. 321-342
    • Drinfel'd, V.G.1
  • 8
    • 0040128734 scopus 로고
    • Quantum groups
    • Proceedings of the International Congress of Mathematicians, Berkeley, California, USA
    • V.G. Drinfel'd, Quantum groups, in: Proceedings of the International Congress of Mathematicians, Berkeley, California, USA, 1987, pp. 798-820.
    • (1987) , pp. 798-820
    • Drinfel'd, V.G.1
  • 9
    • 0001065787 scopus 로고    scopus 로고
    • Lectures on Quantum Groups
    • Amer. Math. Soc., Providence, RI
    • J.C. Jantzen, Lectures on Quantum Groups, in: Grad. Stud. Math., Vol. 6, Amer. Math. Soc., Providence, RI, 1996.
    • (1996) Grad. Stud. Math. , vol.6
    • Jantzen, J.C.1
  • 10
    • 0003462032 scopus 로고
    • Knots and Physics
    • World Scientific, Singapore, 1991
    • L. Kauffman, Knots and Physics, World Scientific, Singapore, 1991, 1994.
    • (1994)
    • Kauffman, L.1
  • 11
    • 0035668851 scopus 로고    scopus 로고
    • Oriented quantum algebras and invariants of knots and links
    • L.H. Kauffman, D.E. Radford, Oriented quantum algebras and invariants of knots and links, J. Algebra 246 (2001) 253-291.
    • (2001) J. Algebra , vol.246 , pp. 253-291
    • Kauffman, L.H.1    Radford, D.E.2
  • 12
    • 0035601436 scopus 로고    scopus 로고
    • Oriented quantum algebras, categories and invariants of knots and links
    • L.H. Kauffman, D.E. Radford, Oriented quantum algebras, categories and invariants of knots and links, J. Knot Theory Ramifications 10 (2001) 1047-1084.
    • (2001) J. Knot Theory Ramifications , vol.10 , pp. 1047-1084
    • Kauffman, L.H.1    Radford, D.E.2
  • 13
    • 43949171690 scopus 로고
    • Algebraic aspects of the quantum Yang-Baxter Equation
    • L.A. Lambe, D.E. Radford, Algebraic aspects of the quantum Yang-Baxter Equation, J. Algebra 154 (1993) 228-288.
    • (1993) J. Algebra , vol.154 , pp. 228-288
    • Lambe, L.A.1    Radford, D.E.2
  • 14
    • 0009114981 scopus 로고    scopus 로고
    • Introduction to the Quantum Yang-Baxter Equation and Quantum Groups: An Algebraic Approach
    • Kluwer Academic, Dordrecht
    • L.A. Lambe, D.E. Radford, Introduction to the Quantum Yang-Baxter Equation and Quantum Groups: An Algebraic Approach, in: Math. Appl., Vol. 423, Kluwer Academic, Dordrecht, 1997.
    • (1997) Math. Appl. , vol.423
    • Lambe, L.A.1    Radford, D.E.2
  • 15
    • 0002229544 scopus 로고
    • Modular representations and quantum groups
    • Beijing, Contemp. Math., Amer. Math. Soc., Providence, RI, 1989
    • G. Lusztig, Modular representations and quantum groups, in: Classical Groups and Related Topics, Beijing, 1987, in: Contemp. Math., Vol. 82, Amer. Math. Soc., Providence, RI, 1989, pp. 59-77.
    • (1987) Classical Groups and Related Topics , vol.82 , pp. 59-77
    • Lusztig, G.1
  • 16
    • 0001940379 scopus 로고
    • Quasitriangular Hopf algebras and Yang-Baxter equations
    • S. Majid, Quasitriangular Hopf algebras and Yang-Baxter equations, Internat. J. Modern Phys. A 5 (1990) 1-91.
    • (1990) Internat. J. Modern Phys. A , vol.5 , pp. 1-91
    • Majid, S.1
  • 17
    • 0003229461 scopus 로고
    • Hopf Algebras and Their Actions on Rings
    • Amer. Math. Soc., Providence, RI
    • S. Montgomery, Hopf Algebras and Their Actions on Rings, in: Reg. Conf. Ser. Math., Vol. 82, Amer. Math. Soc., Providence, RI, 1993.
    • (1993) Reg. Conf. Ser. Math. , vol.82
    • Montgomery, S.1
  • 18
    • 21944432144 scopus 로고    scopus 로고
    • Generalized double crossproducts associated with the quantized enveloping algebras
    • D.E. Radford, Generalized double crossproducts associated with the quantized enveloping algebras, Comm. Algebra 26 (1998) 241-291.
    • (1998) Comm. Algebra , vol.26 , pp. 241-291
    • Radford, D.E.1
  • 19
    • 43949166060 scopus 로고
    • Minimal quasitriangular Hopf algebras
    • D.E. Radford, Minimal quasitriangular Hopf algebras, J. Algebra 157 (1993) 285-315.
    • (1993) J. Algebra , vol.157 , pp. 285-315
    • Radford, D.E.1
  • 20
    • 0346174084 scopus 로고    scopus 로고
    • On quantum algebras and coalgebras, oriented quantum algebras and coalgebras, invariants of 1-1 tangles, knots and links
    • Math. Sci. Inst. Publ., Cambridge Univ. Press, New York
    • D.E. Radford, On quantum algebras and coalgebras, oriented quantum algebras and coalgebras, invariants of 1-1 tangles, knots and links, in: New Directions in Hopf Algebras, in: Math. Sci. Inst. Publ., Vol. 43, Cambridge Univ. Press, New York, 2002, pp. 263-319.
    • (2002) New Directions in Hopf Algebras , vol.43 , pp. 263-319
    • Radford, D.E.1
  • 21
    • 0033555097 scopus 로고    scopus 로고
    • Finite-dimensional simple-pointed Hopf algebras
    • D.E. Radford, Finite-dimensional simple-pointed Hopf algebras, J. Algebra 211 (1999) 686-710.
    • (1999) J. Algebra , vol.211 , pp. 686-710
    • Radford, D.E.1
  • 22
    • 0002112187 scopus 로고
    • Yetter-Drinfel'd categories associated to an arbitrary bialgebra
    • D.E. Radford, J. Towber, Yetter-Drinfel'd categories associated to an arbitrary bialgebra, J. Pure Appl. Algebra 87 (1993) 259-279.
    • (1993) J. Pure Appl. Algebra , vol.87 , pp. 259-279
    • Radford, D.E.1    Towber, J.2
  • 23
    • 0348065520 scopus 로고    scopus 로고
    • Tracelike functionals on the double of the Taft Hopf algebra
    • Preprint
    • D.E. Radford, S. Westreich, Tracelike functionals on the double of the Taft Hopf algebra, Preprint, 2002, 39 p.
    • (2002) , pp. 39
    • Radford, D.E.1    Westreich, S.2
  • 25
    • 85023242894 scopus 로고
    • Noncommutative sequences of divided powers
    • Lecture Notes in Math., Springer-Verlag, Berlin
    • E.J. Taft, Noncommutative sequences of divided powers, in: Conf. Proc., Lie Algebras and Related Topics, in: Lecture Notes in Math., Springer-Verlag, Berlin, 1982.
    • (1982) Conf. Proc., Lie Algebras and Related Topics
    • Taft, E.J.1
  • 26
    • 0001761488 scopus 로고
    • The order of the antipode of finite-dimensional Hopf algebra
    • E.J. Taft, The order of the antipode of finite-dimensional Hopf algebra, Proc. Natl. Acad. Sci. USA 68 (1971) 2631-2633.
    • (1971) Proc. Natl. Acad. Sci. USA , vol.68 , pp. 2631-2633
    • Taft, E.J.1
  • 27
    • 84974224281 scopus 로고
    • Quantum groups and representations of monoidal categories
    • D.N. Yetter, Quantum groups and representations of monoidal categories, Math. Proc. Cambridge Philos. Soc. 108 (1990) 261-290.
    • (1990) Math. Proc. Cambridge Philos. Soc. , vol.108 , pp. 261-290
    • Yetter, D.N.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.