Blattner–Cohen–Montgomery's Duality Theorem for (Weak) Group Smash Products

REFERENCES

• Abuhlail , J. Y. , Gomez-Torrecillas , J. , Lobillo , F. ( 2001 ). Duality and rational modules in Hopf algebras over commutative rings . J. Algebra 240 : 165 – 184 .
   Web of Science ®Google Scholar
• Blattner , R. , Montgomery , S. ( 1985 ). A duality theorem for Hopf module algebras . J. Algebra 95 : 153 – 172 .
   Web of Science ®Google Scholar
• Böhm , G. , Nill , F. , Szlachányi , K. ( 1999 ). Weak Hopf algebras I: Integral theory and C*-structure . J. Algebra 221 : 385 – 438 .
   Web of Science ®Google Scholar
• Caenepeel , S. , De Lombaerde , M. ( 2006 ). A categorical approach to Turaev's Hopf group-coalgebras . Comm. Algebra 34 ( 7 ): 2631 – 2657 .
   Web of Science ®Google Scholar
• Caenepeel , S. , Militaru , G. , Zhu , S. ( 2002 ). Frobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations . Lect. Notes in Math. 1787 . Berlin : Springer Verlag .
   Google Scholar
• Chen , C. Y. , Nichols , W. ( 1990 ). A duality theorem for Hopf module algebras over Dedekind rings . Comm. Algebra 18 : 3209 – 3221 .
   Web of Science ®Google Scholar
• Cohen , M. , Montgomery , S. ( 1984 ). Group-graded rings, smash products, and group actions . Trans. Amer. Math. Soc. 282 : 237 – 258 .
   Web of Science ®Google Scholar
• Doi , Y. ( 1983 ). On the structure of relative Hopf modules . Comm. Algebra 11 : 243 – 255 .
   Web of Science ®Google Scholar
• Doi , Y. ( 1992 ). Unifying Hopf modules . J. Algebra 153 : 373 – 385 .
   Web of Science ®Google Scholar
• Guo , Q. L. , Wang , S. H. ( 2005 ). Weak group corings and weak group entwined modules . Submitted .
   Google Scholar
• Molnar , R. K. (1977). Semi-direct products of Hopf algebras. J. Algebra 47:29–51.
   Web of Science ®Google Scholar
• Nikshych , D. ( 2000 ). A duality theorem for quantum groupoids . Contemp. Math. 267 : 237 – 243 .
   Google Scholar
• Sweedler , M. ( 1969 ). Hopf Algebras . New York : Benjamin .
   Google Scholar
• Turaev , V. G. ( 2000 ). Homotopy field theory in dimension 3 and crossed group-categories . Preprint .
   Google Scholar
• Van Daele , A. ( 1994 ). Multiplier Hopf algebras . Trans. Amer. Math. Soc. 342 ( 2 ): 917 – 932 .
   Web of Science ®Google Scholar
• Van Daele , A. ( 1998 ). An algebraic framework for group duality . Adv. Math. 140 : 323 – 366 .
   Web of Science ®Google Scholar
• Van Daele , A. , Wang , S. H. ( 2004a ). Multiplier unifying Hopf algebras . Preprint. 2004. K.U. Leuven. Submitted for publication .
   Google Scholar
• Van Daele , A. , Wang , S. H. ( 2004b ). New braided crossed categories and Drinfel'd quantum double for weak Hopf π-coalgebras . Preprint. 2004. K.U. Leuven. To appear in 2008 Comm. Algebra .
   Google Scholar
• Van den Bergh , M. ( 1984 ). A duality theorem for Hopf algebras . In: Methods in Ring Theory . Dordrecht, NATO Sci. Ser. C, vol. 129 , pp. 517 – 522 .
   Google Scholar
• Virelizier , A. ( 2002 ). Hopf group-coalgebras . J. Pure and Applied Algebra 171 : 75 – 122 .
   Web of Science ®Google Scholar
• Virelizier , A. ( 2005 ). Graded quantum groups and quasitriangular Hopf group-coalgebras . Comm. Algebra 33 ( 9 ): 3029 – 3050 .
   Web of Science ®Google Scholar
• Wang , S. H. ( 2004a ). Group entwining structures and group coalgebra Galois extensions . Comm. Algebra 32 ( 9 ): 3417 – 3436 .
   Web of Science ®Google Scholar
• Wang , S. H. ( 2004b ). Group twisted samsh products and Doi-Hopf modules for T-coalgebras . Comm. Algebra 32 ( 9 ): 3437 – 3458 .
   Web of Science ®Google Scholar
• Wang , S. H. ( 2004c ). A Maschke Type Theorem for Hopf π-Comodules . Tsukuba J. Math. 28 ( 2 )( 2004 ): 377 – 388 .
   Google Scholar
• Wang , S. H. ( 2006 ). Morita Contexts, π-Galois Extensions for Hopf π-coalgebras . Comm. Algebra 34 ( 2 ): 521 – 546 .
   Web of Science ®Google Scholar
• Zhang , L. Y. , Zhu , S. L. ( 2004 ). Fundamental theorems of weak Doi-Hopf modules and semisimple weak smash product Hopf algebras . Comm. Algebra 32 ( 9 ): 3403 – 3416 .
   Web of Science ®Google Scholar
• Zunino , M. ( 2004a ). Double construction for crossed Hopf coalgebra . J. Algebra 278 : 43 – 75 .
   Web of Science ®Google Scholar
• Zunino , M. ( 2004b ). Yetter–Drinfel'd modules for crossed structures . J. Pure and Applied Algebra 193 ( 1–3 ): 313 – 343 .
   Web of Science ®Google Scholar
• Communicated by M. Cohen.
   Google Scholar