Doi–Hopf Modules and Yetter–Drinfeld Modules for Quasi-Hopf Algebras

REFERENCES

• Brzeziński , T. ( 2002 ). The structure of corings. Induction functors, Maschke-type theorem, and Frobenius and Galois properties . Algebr. Representat. Theory 5 : 389 – 410 . [CSA]
   Web of Science ®Google Scholar
• Brzeziński , T. , Wisbauer , R. ( 2003 ). Corings and Comodules . London Math. Soc. Lect. Note Ser. 309 . Cambridge : Cambridge University Press .
   Google Scholar
• Bulacu , D. , Nauwelaerts , E. ( 2000 ). Relative Hopf modules for (dual) quasi Hopf algebras . J. Algebra 229 : 632 – 659 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Bulacu , D. , Caenepeel , S. ( 2003 ). Two-sided two-cosided Hopf modules and Doi–Hopf modules for quasi-Hopf algebras . J. Algebra 270 ( 1 ): 55 – 95 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Bulacu , D. , Panaite , F. , Van Oystaeyen , F. ( 2004 ). Generalized diagonal crossed products and smash products for (quasi) Hopf algebras , preprint . [CSA]
   Google Scholar
• Bulacu , D. , Caenepeel , S. , Panaite , F. ( 2005 ). More properties of Yetter–Drinfeld modules over quasi-Hopf algebras . In: Caenepeel , S. , Van Oystaeyen , F. , eds. Hopf Algebras in Non-Commutativegeometry and Physics . Lecture Notes Pure Appl. Math. 239 . New York : Dekker , pp. 89 – 112 .
   Google Scholar
• Bulacu , D. , Caenepeel , S. , Panaite , F. ( 2006 ). Yetter–Drinfeld categories for quasi-Hopf algebras . Comm. Algebra 34 : 1 – 35 . [CSA]
   Web of Science ®Google Scholar
• Caenepeel , S. , Militaru , G. , Zhu , S. ( 1997 ). Crossed modules and Doi–Hopf modules . Israel J. Math. 100 : 221 – 247 . [CSA]
   Web of Science ®Google Scholar
• Dăscălescu , S. , Năstăsescu , C. , Torrecillas , B. (1999). Co-Frobenius Hopf algebras: integrals, Doi–Koppinen modules and injective objects. J. Algebra 220:542–560. [CSA] [CROSSREF]
   Google Scholar
• Dăscălescu , S. , Năstăsescu , C. , Raianu , Ş. ( 2001 ). Hopf Algebras: An Introduction . Monographs Textbooks in Pure Appl. Math. 235 . New York : Dekker .
   Google Scholar
• Doi , Y. ( 1994 ). Generalized smash products and Morita contexts for arbitrary Hopf algebras . In Bergen , J. , Montgomery , S. , eds. Advances in Hopf Algebras . Lecture Notes Pure Appl. Math. 158 . New York : Dekker , pp. 39 – 53 .
   Google Scholar
• Drinfeld , V. G. ( 1990 ). Quasi-Hopf algebras . Leningrad Math. J. 1 : 1419 – 1457 . [CSA]
   Google Scholar
• El Kaoutit , L. , Gómez-Torrecillas , J. , Lobillo , F. ( 2004 ). Semisimple corings . Algebra Colloquium 11 ( 4 ): 427 – 442 . [CSA]
   Google Scholar
• Hausser , F. , Nill , F. ( 1999 ). Diagonal crossed products by duals of quasi-quantum groups . Rev. Math. Phys. 11 : 553 – 629 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Kassel , C. ( 1995 ). Quantum Groups . Graduate Texts in Mathematics 155 . Berlin : Springer Verlag .
   Google Scholar
• Koppinen , M. ( 1994 ). Variations on the smash product with applications to group-graded rings . J. Pure Appl. Algebra 104 : 61 – 80 . [CSA] [CROSSREF]
   Google Scholar
• Majid , S. ( 1995 ). Foundations of Quantum Group Theory . Cambridge : Cambridge Univ. Press .
   Google Scholar
• Majid , S. ( 1998 ). Quantum double for quasi-Hopf algebras . Lett. Math. Phys. 45 : 1 – 9 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Menini , C. , Zuccoli , M. ( 1997 ). Equivalence theorems and Hopf-Galois extensions . J. Algebra 194 : 245 – 274 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Schauenburg , P. ( 2002 ). Hopf modules and the double of a quasi-Hopf algebra . Trans. Amer. Math. Soc. 354 : 3349 – 3378 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Sweedler , M. E. ( 1969 ). Hopf Algebras . New York : Benjamin .
   Google Scholar
• Wisbauer , R. ( 1991 ). Foundations of Module and Ring Theory . Philadelphia : Gordon and Breach .
   Google Scholar
• Communicated by A. Facchini.
   Google Scholar