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  • 1 College of Science, Nanjing Agricultural University, Nanjing 210095, P.R. China
  • 2 College of Mathematics and Information Technology, Nanjing Xiaozhuang University, Nanjing 211171, P.R. China
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Abstract

We obtain the structure theorem for -Hopf bimodules over Hopf algebroids, where H is the total algebra of the Hopf algebroid . Based on this theorem, we investigate the structure theorem for comodule algebras over Hopf algebroids.

  • [1] Militaru, G., Stefan, D. 1994 Extending modules for Hopf Galois extensions Comm. Algebra 22 56575678 .

  • [2] Panaite, F., Oystaeyen Van, F. 2007 A structure theorem for quasi-Hopf comodule algebras Proc. Amer. Math. Soc. 135 16691677 .

  • [3] Böhm, G., Szlachányi, K. 2004 Hopf algebroids with bijective antipodes: axioms, integrals and duals J. Algebras 274 708750 .

  • [4] Böhm, G. 2005 An Alternative Notion of Hopf Algebroids Lect. Notes Pure Appl. Math. 239 New York.

  • [5] Böhm, G. 2005 Integral theory for Hopf algebroids Algebr. Repesent. Th. 8 563599 . Corrigendum, doi:10.1007/s10468-009-9167-0.

  • [6] Takeuchi, M. 1977 Groups of algebras over J. Math. Soc. Japan 29 459492 .

  • [7] Lu, J. H. 1996 Hopf algebroids and quantum groupoids Internat. J. Math. 7 4770 .

  • [8] Xu, P. 2001 Quantum groupoids Comm. Math. Phys. 216 539581 .

  • [9] Kadison, L., Szlachányi, K. 2003 Bialgebroid actions on depth two extensions and duality Adv. Math. 179 75121 .

  • [10] Böhm, G., Nill, F., Szlachányi, K. 1999 Weak Hopf algebras I. Integral theory and C -structure J. Algebra 221 385438 .

  • [11] Böhm, G. 2009 Hopf Algebroids Handbook of Algebra 6 Elsevier.

  • [12] Morava, J. 1985 Noetherian localisations of categories of cobordism comodules Ann. Math. 121 139 .

  • [13] Mrc̆un, J. 2001 The Hopf algebroids of functions on étale groupoids and their principal Morita equivalence J. Pure Appl. Algebra 160 249262 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [14] Ardizzoni, A., Böhm, G., Menini, C. 2007 A Schneider type theorem for Hopf algebroids J. Algebra 318 225269 .

  • [15] Sweedler, M. E. 1975 Groups of simple algebras I.H.E.S., Publ. 44 79189.

  • [16] Sweedler, M. E. 1975 The predual theorem to the Jacobson-Bourbaki theorem Trans. Amer. Math. Soc. 213 391406 .

  • [17] Brzeziński, T., Wisbauer, R. 2003 Corings and Comodules Cambridge University Press Cambridge . http://www.maths.swan.ac.uk/staff/tb/corings.htm.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [18] Böhm, G., Brzeziński, T. 2006 Cleft extensions of Hopf algebroids Appl. Categor. Struct. 14 431469 . Corrigendum, 17 (2009), 613–620.

  • [19] Böhm, G. 2005 Galois theory for Hopf algebroids Ann. Univ. Ferrara-Sez. VII-Sc. Mat. LI 233262.

  • [20] Böhm, G. 2006 Galois extensions over commutative and noncommutative base Caenepeel, S., Oystaeyen Van, F. (eds.) New Techniques in Hopf Algebras and Graded Ring Theory http://arxiv.org/abs/math/0701064v2.

    • Search Google Scholar
    • Export Citation
  • [21] Böhm, G., Vercruysse, J. 2009 Corrigendum to “Morita theory for coring extensions and cleft bicomodules” [Adv. Math., 209 (2007), 611–648] Adv. Math. 221 682686 .

    • Crossref
    • Search Google Scholar
    • Export Citation

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