The Antipode of a Braided Dual Quasi-Hopf Algebra is Bijective

REFERENCES

• Bulacu , D. , Caenepeel , S. ( 2003 ). Integrals for (dual) quasi-Hopf algebras. Applications . J. Algebra 266 : 552 – 583 .
   Web of Science ®Google Scholar
• Bulacu , D. , Caenepeel , S. , Panaite , F. ( 2006 ). Yetter–Drinfeld categories for quasi-Hopf algebras . Comm. Algebra 34 : 1 – 35 .
   Web of Science ®Google Scholar
• Bulacu , D. , Caenepeel , S. , Torrecillas , B. ( 2006 ). Doi-Hopf modules and Yetter–Drinfeld modules for quasi-Hopf algebras . Comm. Algebra 34 : 3413 – 3449 .
   Web of Science ®Google Scholar
• Bulacu , D. , Nauwelaerts , E. ( 2000 ). Relative Hopf modules for (dual) quasi-Hopf algebras . J. Algebra 229 : 632 – 659 .
   Web of Science ®Google Scholar
• Bulacu , D. , Nauwelaerts , E. ( 2003 ). Dual quasi-Hopf algebra coactions, smash coproducts and relative Hopf modules . Rev. Roumaine Math. Pures Appl. 47 : 415 – 443 .
   Google Scholar
• Bulacu , D. , Panaite , F. , Van Oystaeyen , F. ( 2006 ). Generalized diagonal crossed products and smash products for quasi-Hopf algebras applications . Comm. Math. Phys. 266 : 355 – 399 .
   Web of Science ®Google Scholar
• Doi , Y. ( 1993 ). Braided bialgebras and quadratic bialgebras . Comm. Algebra 21 : 1731 – 1749 .
   Web of Science ®Google Scholar
• Drinfeld , V. G. ( 1990a ). Quasi-Hopf algebras . Leningrad Math. J. 1 : 1419 – 1457 .
   Google Scholar
• Drinfeld , V. G. ( 1990a ). Quasi-Hopf algebras and the Knizhnik–Zamolodchikov equations . In: et al. , eds. Problems of Modern Quantum Field Theory . New York : Springer-Verlag , pp. 1 – 13 .
   Google Scholar
• Li , J. Q. ( 2006 ). Dual quasi-Hopf algebras and antipodes . Algebra Colloquium 13 : 111 – 118 .
   Google Scholar
• Majid , S. ( 1995 ). Foundations of Quantum Group Theory . Cambridge : Cambridge Univ. Press .
   Google Scholar
• Montgomery , S. ( 1993 ). Hopf algebras and their actions on rings. CBMS Lectures in Mathematics 82. Providence, RI: AMS .
   Google Scholar
• Panaite , F. , Van Oystaeyen , F. ( 2007 ). L-R-smash product for (quasi-)Hopf algebras . J. Algebra 309 : 168 – 191 .
   Web of Science ®Google Scholar
• Sweedler , M. ( 1969 ). Hopf Algebra . New York : Benjamin .
   Google Scholar
• Communicated by C. Cibils.
   Google Scholar