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Original Articles

The Duality Theorem for Weak Hopf Algebra (Co) Actions

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Pages 4613-4632 | Received 29 Sep 2008, Published online: 20 Jan 2011

REFERENCES

  • Alonso Álvarez , J. N. , Fernández Vilaboa , J. M. , González Rodríguez , R. , Rodríguez Raposo , A. B. ( 2006 ). Weak C-cleft extensions and weak Galois extensions . J. Algebra 299 : 276 – 293 .
  • Blattner , R. , Montgomery , S. ( 1985 ). A duality theorem for Hopf module algebras . J. Algebra 95 : 153 – 172 .
  • Beattie , M. ( 1992 ). On the Blattner–Montgomery duality theorem for Hopf algebras . Contemp. Math. 124 : 23 – 28 .
  • Böhm , G. , Nill , F. , Szlachanyi , K. ( 1999 ). Weak Hopf algebras I: Integral theory and C*-structure . J. Algebra 221 : 385 – 438 .
  • Caenepeel , S. , De Groot , E. ( 2000 ). Modules over weak entwining structures . Contemp. Math. 267 : 31 – 54 .
  • Caenepeel , S. , De Groot , E. ( 2007 ). Galois theory for weak Hopf algebras . Rev. Roumaine Math. Pures Appl. 52 : 51 – 76 .
  • Kreimer , H. K. , Takeuchi , M. ( 1981 ). Hopf algebras and Galois extensions . Indiana Univ. Math. J. 30 : 675 – 692 .
  • Nikshych , D. ( 2000 ). A duality theorem for quantum groupoids . Contemp. Math. 267 : 237 – 243 .
  • Nikshych , D. ( 2002 ). On the structure of weak Hopf algebras . Adv. in Math. 170 : 257 – 286 .
  • Nikshych , D. , Vainerman , L. ( 2002 ). Finite quantum groupoids and their applications . In: New Directions in Hopf Algebras . Vol. 43 . MSRI Publications , pp. 211 – 262 .
  • Nikshych , D. , Turaev , V. , Vainerman , L. ( 2003 ). Invariants of knots and 3-manifolds from quantum groupoids . Topology and Its Application 127 : 91 – 123 .
  • Szlachányi , K. (2004). The double algebraic viewpoint of finite quantum groupoids. J. Algebra 280:249–294.
  • Sweedler , M. E. ( 1969 ). Hopf Algebra . New York : Benjamin .
  • Takesaki , M. ( 1972 ). Duality and von Neumann algebras . In: Hofmann , K. H. , ed. Lecture on Operator Algebras . Lecture notes in Math. , 247. Berlin : Springer-Verlag , pp. 666 – 779 .
  • Wang , S. H. ( 2004 ). Cibils–Rosso's theorem for quantum groupoids . Comm. Algebra 32 ( 9 ): 3703 – 3722 .
  • Communicated by J. Alev.

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