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Communications in Algebra Volume 30, 2002 - Issue 7
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Original Articles

COMPACT MATRIX QUANTUM GROUPS ARISING FROM HERMITIAN YANG-BAXTER COALGEBRAS

Andrés Abella Centro de Matemática, Universidad de la República, Igua 4225 (11400), Montevideo, Uruguay
&
Nicolás Andruskiewitsch Universidad Nacional de Córdoba, Astronomía y Física, (5000) C. Universitaria, Co´rdoba, Argentina
Pages 3107-3142 | Received 01 Jun 1999, Published online: 01 Feb 2007

REFERENCES

  • Abella , A. and Andruskiewitsch , N. 1999 . Compact Quantum Groups Arising from the FRT-Construction . Bol. Acad. Ciencias (Co´rdoba) , 63 : 15 – 44 .
  • Dijkhuizen , M. and Koornwinder , T. 1994 . CQG Algebras: A Direct Algebraic Approach to Compact Quantum Groups . Lett. Math. Phys. , 32 ( 4 ) : 315 – 330 .
  • Doi , Y. 1993 . Braided Bialgebras and Quadratic Bialgebras . Commun. Alg. , 21 : 1731 – 1750 .
  • Fadeev , L. , Reshetikhin , N. and Takhtajan , L. 1990 . Quantization of Lie Groups and Lie Algebras . Leningrad J. of Math. , 1 : 193 – 225 .
  • Gurevich , D. 1991 . Algebraic Aspects of the Quantum Yang--Baxter Equation . Leningrad J. of Math. , 2 : 801 – 828 .
  • Hayashi , T. 1992 . Quantum Groups and Quantum Determinants . J. Algebra , 152 : 146 – 165 .
  • Hayashi , T. 1994 . Quantum Groups and Quantum Semigroups . J. Algebra , 204 : 225 – 254 .
  • Humphreys , J.E. 1972 . Introduction to Lie Algebras and Representation Theory New York : Springer-Verlag .
  • Larson , R.G. and Towber , J. 1991 . Two Dual Classes of Bialgebras Related to the Concepts of “Quantum Group” and “Quantum Lie Algebra” . Commun. Alg. , 19 : 3295 – 3345 .
  • Lusztig , G. 1988 . Quantum Deformations of Certain Simple Modules over Enveloping Algebras . Adv. in Math. , 70 : 237 – 249 .
  • Lyubashenko , V. 1986 . Hopf Algebras and Vector Symmetries . Russian Math. Surveys , 41 : 153 – 154 .
  • Majid , S. 1990 . Quasi-triangular Hopf Algebras and Yang-Baxter Equations . Int. J. Mod. Phys. , 5 : 1 – 91 .
  • Manin , Yu. I. 1988 . “ Montreal Univ. CRM-1561 ” . In Quantum Groups and Noncommutative Geometry Montreal
  • Reshetikhin , N. 1990 . Quantized Universal Algebras, the Yang-Baxter Equation and Invariants of Links. I . LOMI Preprints , E-4-87 : 1 – 68 .
  • Rosso , M. 1990 . Analogues de la forme de Killing et du Theoreme d'Harish-Chandra pour les Groupes Quantiques . Ann. Sci. Ec. Norm. Super. , 23 : 445 – 467 .
  • Schauenburg , P. 1992 . On Coquasitriangular Hopf Algebras and the Quantum Yang-Baxter equation . Algebra Berichte , 67 : 1 – 76 . Verlag R. Fischer, Munchen
  • Takeuchi , M. 1971 . Free Hopf Algebras Generated by coalgebras . J. Math. Soc. Japan , 23 : 561 – 582 .
  • Takeuchi , M. 1990 . Matric Bialgebras and Quantum Groups . Israel J. of Maths , 72 : 232 – 251 .
  • Takeuchi , M. 2000 . The Coquasitriangular Hopf Algebra Asociated with a Rigid Yang-Baxter Coalgebra . Lecture Notes in Pure and Appl. Math. , 209

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