Galois Extensions for Coquasi-Hopf Algebras

REFERENCES

• Albuquerque , H. , Majid , S. ( 1999 ). Quasialgebra structure of the octonions . J. Algebra 220 : 188 – 224 .
   Web of Science ®Google Scholar
• Albuquerque , H. , Majid , S. ( 1999 ). Z n -quasialgebras. In: Matrices and Group Representations. Proceedings of a Workshop Dedicated to Professor Graciano N. De Oliveira on the Occasion of his 60th Birthday, Coimbra, Portugal, May 6–8, 1998. Volume 19 of Textos Math., Ser. , Coimbra : Univ. de Coimbra, Departamento de Matemática , pp. 57 – 64 .
   Google Scholar
• Altschuler , D. , Coste , A. ( 1992 ). Quasi-quantum groups, knots, three manifolds and topological field theory . Comm. Math. Phys. 150 : 83 – 107 .
   Web of Science ®Google Scholar
• Ardizzoni , A. , Menini , C. , Stefan , D. ( 2007 ). Hochschild cohomology and smoothness in monoidal categories . J. Pure Appl. Algebra 208 : 297 – 330 .
   Web of Science ®Google Scholar
• Balan , A. ( 2008 ). Crossed products for coquasi-Hopf algebras . Arabian J. Sci. Eng. 33 : 53 – 84 .
   Google Scholar
• Balan , A. ( 2009 ). A Morita context and Galois extensions for quasi-Hopf algebras . Comm. Algebra 37 ( 4 ): 1129 – 1150 .
   Web of Science ®Google Scholar
• Beattie , M. , Iovanov , M. , Raianu , Ş. ( 2009 ). The antipode of a dual quasi-Hopf algebra with nonzero integrals is bijective . Alg. Repr. Theory 12 ( 2–5 ): 251 – 255 .
   Google Scholar
• Blattner , R. J. , Montgomery , S. ( 1989 ). Crossed products and Galois extensions of Hopf algebras . Pacific J. Math. 137 : 37 – 54 .
   Web of Science ®Google Scholar
• Böhm , G. ( 2005 ). Galois theory for Hopf algebroids . Ann. Univ. Ferrara, Nuova Ser., Sez. VII 51 : 233 – 262 .
   Google Scholar
• Brzèzinski , T. , Hajac , P. M. ( 1999 ). Coalgebra extensions and algebra coextensions of Galois type . Comm. Algebra 27 : 1347 – 1367 .
   Web of Science ®Google Scholar
• Brzezinski , T. , Militaru , G. ( 2002 ). Bialgebroids, × A -bialgebras and duality . J. Algebra 251 ( 1 ): 279 – 294 .
   Web of Science ®Google Scholar
• Bulacu , D. ( 1999 ). On the antipode of semi-Hopf algebras and braided semi-Hopf algebras . Rev. Roum. Math. Pures Appl. 44 ( 3 ): 329 – 340 .
   Google Scholar
• Bulacu , D. , Chirita , B. ( 2002 ). Dual drinfeld double by diagonal crossed product . Rev. Roum. Math. Pures Appl. 47 ( 3 ): 271 – 294 .
   Google Scholar
• Bulacu , D. , Nauwelaerts , E. (2000). Relative Hopf modules for (dual) quasi-Hopf algebras. J. Algebra 229(2):632–659.
   Web of Science ®Google Scholar
• Bulacu , D. , Nauwelaerts , E. ( 2002 ). Dual quasi-Hopf algebra coactions, smash coproducts and relative Hopf modules . Rev. Roum. Math. Pures Appl. 47 ( 4 ): 415 – 443 .
   Google Scholar
• Chase , S. U. , Harrison , D. K. , Rosenberg , A. ( 1965 ). Galois Theory and Cohomology of Commutative Rings . Number 52 in AMS Memoirs. Providence , RI : AMS .
   Google Scholar
• Chase , S. U. , Sweedler , M. E. ( 1969 ). Hopf algebras and Galois theory . Number 97 in Lect. Notes in Math . Berlin : Springer-Verlag .
   Google Scholar
• Doi , Y. , Takeuchi , M. ( 1986 ). Cleft comodule algebras for a bialgebra . Comm. Alg. 14 : 801 – 818 .
   Web of Science ®Google Scholar
• Doi , Y. , Takeuchi , M. ( 1989 ). Hopf-Galois extensions of algebras, the Miyashita–Ulbrich action, and Azumaya algebras . J. Algebra 121 ( 2 ): 488 – 516 .
   Web of Science ®Google Scholar
• Drinfeld , V. G. ( 1990 ). Quasi-Hopf algebras . Leningrad Math. J. 1 : 1419 – 1457 .
   Google Scholar
• Dăscălescu , S. , Năstăsescu , C. , Raianu , Ş. ( 2001 ). Hopf Algebras: An Introduction . Number 235 in Pure and Applied Math . New York : Marcel Dekker .
   Google Scholar
• Kadison , L. , Szlachanyi , K. ( 2003 ). Bialgebroid actions on depth two extensions and duality . Adv. Math. 179 : 75 – 121 .
   Web of Science ®Google Scholar
• Kassel , C. ( 1995 ). Quantum Groups . Number 155 in Graduate Texts in Math . New York : Springer Verlag .
   Google Scholar
• Kreimer , H. F. , Takeuchi , M. ( 1981 ). Hopf algebras and Galois extensions of an algebra . Indiana Math. J. 30 : 675 – 692 .
   Web of Science ®Google Scholar
• Majid , S. ( 1992 ). Tannaka-Krein theorem for quasi-Hopf algebras . In: Gestenhaber , M. , Stasheff , J. , eds. Deformation Theory and Quantum Groups with Applications to Mathematical Physics, Amherst, MA, 1990 . Volume 134 of Contemp. Math. Providence , RI : Amer. Math. Soc. , pp. 219 – 232 .
   Google Scholar
• Majid , S. ( 1995 ). Foundations of Quantum Group Theory . Cambridge : Cambridge University Presss .
   Google Scholar
• Masuoka , A. ( 2003 ). More homological approach to composition of subfactors . J. Math. Sci., Tokyo 10 ( 4 ): 599 – 630 .
   Google Scholar
• Panaite , F. , Ştefan , D. ( 1997 ). When is the category of comodules a braided tensor category? Rev. Roum. Math. Pures Appl. 42 ( 1–2 ): 107 – 119 .
   Google Scholar
• Pareigis , B. ( 1977 ). Non-additive ring and module theory I. General theory of monoids . Publ. Math. Debrecen 24 : 189 – 204 .
   Google Scholar
• Pareigis , B. ( 1977 ). Non-additive ring and module theory II . C-categories, C-functors and C-morphisms. Publ. Math. Debrecen 24 : 351 – 361 .
   Google Scholar
• Schauenburg , P. ( 1998 ). Bialgebras over noncommutative rings and a structure theorem for Hopf bimodules . Appl. Cat. Str. 6 : 193 – 222 .
   Web of Science ®Google Scholar
• Schauenburg , P. ( 2003 ). Actions of monoidal categories, and generalized Hopf smash products . J. Alg. 270 : 521 – 563 .
   Web of Science ®Google Scholar
• Schauenburg , P. ( 2004 ). Hopf-Galois and Bi-Galois extensions . In: Janelidze , G. , Pareigis , B. , Tholen , W. , eds. Galois Theory, Hopf Algebras, and Semiabelian Categories . Volume 43 of Fields Inst. Commun. Providence , RI : AMS .
   Google Scholar
• Schneider , H.-J. ( 1990 ). Principal homogeneous spaces for arbitrary Hopf algebras . Israel J. Math. 72 ( 1–2 ): 167 – 195 .
   Web of Science ®Google Scholar
• Schneider , H.-J. ( 1990 ). Representation theory of Hopf Galois extensions . Israel J. Math. 72 ( 1–2 ): 196 – 231 .
   Google Scholar
• Ulbrich , K. H. ( 1981 ). Vollgraduierte algebren . Abh. Math. Sem. Univ. Hamburg 51 : 136 – 148 .
   Web of Science ®Google Scholar
• Communicated by M. Cohen.
   Google Scholar