80
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

The Quantum Double for Quasitriangular Quasi-Hopf Algebras

&
Pages 1403-1425 | Received 01 Nov 2001, Published online: 31 Aug 2006

References

  • Altschuler , D. and Coste , A. 1992 . Quasi-quantum groups, knots, three-manifolds, and topological field theory . Comm. Math. Phys. , 150 : 83 – 107 .
  • Bulacu , D. and Panaite , F. 1998 . A generalization of the quasi-Hopf algebra D ω (G) . Comm. Algebra , 26 : 4125 – 4141 .
  • Bulacu , D. , Panaite , F. and Van Oystaeyen , F. 2000 . Quasi-Hopf algebra actions and smash product . Comm. Algebra , 28 : 631 – 651 .
  • Bulacu , D. and Nauwelaerts , E. 2002 . Radford's biproduct for quasi-Hopf algebras and bosonization . J. Pure Appl. Algebra , 179 : 1 – 42 .
  • Bulacu , D. and Nauwelaerts , E. 2003 . Quasitriangular and ribbon quasi-Hopf algebras . Comm. Algebra , 31 ( 2 ) : 1 – 16 .
  • Drinfeld , V. G. 1987 . “ Quantum groups ” . In Proc. ICM at Berkeley 798 – 820 . Providence : Amer. Math. Soc. .
  • Drinfeld , V. G. 1990a . Quasi-Hopf algebras . Leningrad Math. J. , 1 : 1419 – 1457 .
  • Drinfeld , V. G. 1990b . On quasitriangular quasi-Hopf algebras and a group closely connected with Gal ( ℚ¯ /ℚ) . Algebra i Analiz. , 2 ( 4 ) : 149 – 181 .
  • Hausser , F. and Nill , F. 1999a . Diagonal crossed products by duals of quasi-quantum groups . Rev. Math. Phys. , 11 : 553 – 629 .
  • Hausser , F. and Nill , F. 1999b . Doubles of quasi-quantum groups . Comm. Math. Phys. , 199 : 547 – 589 .
  • Kassel , C. 1995 . “ Quantum Groups ” . In Graduate Texts in Mathematics Vol. 155 , New York : Springer-Verlag .
  • Kirilov , A. N. and Reshetikhin , Y. 1990 . q-Weyl group and a multiplicative formula for universal R-matrices . Comm. Math. Phys. , 134 : 421 – 431 .
  • Levendorsky , S. Z. and Soibelman , Ya. S. 1990 . Some applications of the quantum Weyl groups . J. Geom. Phys. , 7 : 241 – 254 .
  • Majid , S. 1990 . Physics for algebraists: noncommutative and noncocommutative Hopf algebras by a bicrossproduct construction . J. Algebra , 130 : 17 – 64 .
  • Majid , S. 1991 . Doubles of quasitriangular Hopf algebras . Comm. Algebra , 19 : 3061 – 3073 .
  • Majid , S. 1998 . Quantum double for quasi-Hopf algebras . Lett. Math. Phys. , 45 : 1 – 9 .
  • Majid , S. 1994 . “ Algebras and Hopf algebras in braided categories ” . In Advances in Hopf algebras , Lecture Notes Pure Appl. Math. Edited by: Bergen , J. and Montgomery , S. Vol. 158 , New York : Marcel Dekker .
  • Majid , S. 1995 . Foundations of Quantum Group Theory Cambridge Univ. Press .
  • Mac Lane , S. 1997 . “ Categories for the Working Mathematician ” . In Graduate Texts in Mathematics Vol. 5 , New York : Springer-Verlag .
  • Radford , D. 1985 . The structure of Hopf algebras with a projection . J. Algebra , 92 : 322 – 347 .
  • Sweedler , M. E. 1969 . Hopf Algebras New York : Benjamin .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.