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Original Articles

Quantum algebras, quantum coalgebras, invariants of 1-1 tangles and knots

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Pages 5101-5156 | Received 01 Sep 1998, Published online: 27 Jun 2007

References

  • Abe , E. 1980 . Hopf Algebras , Vol. 74 , Cambridge, , UK : Cam­bridge University Press . Cambridge Tracts in Mathematics
  • Doi , Yukio . 1993 . Braided bialgebras and quadratic algebras . Comm. in Alge­bra , 21 : 1731 – 1749 .
  • Drinfel'd , V.G. 1990 . On almost cocommutative Hopf algebras . Leningrad Math J , 1 : 321 – 342 . (translation)
  • Drinfel'd , V.G. 1987 . Quantum Groups . Proceedings of the International Congress of Mathematicians . 1987 , Berkeley, California, USA. pp. 798 – 820 .
  • Kauffman , Louis . 1993 . Gauss Codes, quantum groups and ribbon Hopf alge­bras . Reviews in Math, Physics , 5 : 735 – 773 .
  • Kauffman , Louis . 1994 . Knots and Physics , London, , Singapore : World Scientific . Hong Kong, (1991)
  • Kauffman , Louis H. and Radford , David E. 1993 . A necessary and sufficient condition for a finite-dimensional Drinfel'd double to be a ribbon Hopf algebra . J. of Algebra , 159 : 98 – 114 .
  • Kauffman , Louis H. and Radford , David E. 2000 . A separation result for quan­tum coalgebras with an application to pointed quantum coalgebras of small dimension . J. of Algebra , 225 : 162 – 200 .
  • Kauffman , Louis H. and Radford , David E. 1995 . Invariants of 3-manifolds derived from finite-dimensional Hopf algebras . J. Knot Theory Ramifi­cations , 4 : 131 – 162 .
  • Louis Kauffman L. Radford David E. On invariants of knots and links which arise from quantum coalgebras in preparation
  • Kauffman , Louis H. and Radford , David E. 2000 . “ Oriented quantum algebras and coalgebras ” . In invariants of knots and links preprint
  • Kauffman , Louis H. and Radford , David E. 2000 . Oriented quantum algebras and invariants of knots and links preprint
  • Kauffman , Louis H. and Radford , David E. 2000 . “ Oriented quantum algebras ” . In categories and invariants of knots and links preprint
  • Kauffman , Louis H. and Radford , David E. 1999 . Quantum algebra structures on nxn matrices . J. of Algebra , 213 : 405 – 436 .
  • Kauffman , Louis H. and Radford , David E. 1998 . CentraJity and the KRH invariant . J. Knot Theory Ramifications , 7 : 571 – 624 .
  • Lambe , Larry A. and Radford , David E. 1997 . Introduction to the Quantum Yang-Baxter Equation and Quantum Groups: An algebraic Approach , Boston : Kluwer Academic Publishers . Dordrecht/London
  • Majid , S. 1990 . Physics for algebraists: non-commutative and non-cocommutative Hopf algebras by a bicrossproduct construction . J. of Algebra , 129 : 1 – 91 .
  • Majid , Shahn . 1990 . Quasitriangular Hopf algebras and Yang-Baxter equa­tions . Int. J. Mod. Physics A , 5 : 1 – 91 .
  • Montgomery , S. Hopf Algebras and their actions on rings . Regional Conference Series in Mathematics . Vol. 82 , Providence, RI : AMS .
  • Radford , D.E. 1993 . Minimal quasitriangular Hopf algebras . J. Algebra , 157 : 285 – 315 .
  • Radford , D.E. 2000 . On a parameterized family of twist quantum coalgebras and the bracket polynomial . J. of Algebra , 225 : 93 – 123 .
  • Radford , D.E. 1992 . In Advances in Hopf algebras , 205 – 266 . New York : Dekker . (Chicago, R 1992)148of Lecture Notes in Pure and Applied Math
  • Radford , D.E. 1992 . On the antipode of a quasitriangular Hopf algebra . J, Algebra , 151 : 1 – 11 .
  • Radford , D.E. 1992 . On quantum algebras and coalgebras, oriented quantum algebras and coalgebras . Invariants of 1-1 tangles,knots and links , 151 in preparation
  • Radford , D.E. 1976 . The order of the antipode of a finite-dimensional Hopf algebra is finite . Amer. J. Math , 98 : 333 – 355 .
  • Reshetikhin , N.Yu and Turaev , V.G. 1991 . Invariants of 3-manifolds via link polynomials and quantum groups . Invent Math , 103 : 547 – 597 .
  • Reshetikhin , N.Yu and Turaev , V.G. 1990 . Ribbon graphs and their invari­ants derived from quantum groups . Gomm. Math. Physics , 127 : 1 – 26 .
  • Sehauenburg , P. 1992 . On eoquasitriangular Hopf algebras and the quantum Yang-Baxter equation . Algebra Berichte , 67 : 1 – 76 .
  • Sommerhäuser , Yorck . 1998 . On Kaplansky's fifth conjecture . J. of Algebra , 204 : 202 – 224 .
  • Sweedler , M.E. 1969 . Hopf Algebras , New York : Benjamin .
  • Yetter , D.N. 1990 . Quantum groups and representations of monoidal cate­gories . Math, Proc. Camb. Philos. Soc , 108 : 261 – 290 .

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