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Strong connections and invertible weak entwining structures

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Abstract

In this paper we obtain a criterion under which the bijectivity of the canonical morphism of a weak Galois extension associated to a weak invertible entwining structure is equivalent to the existence of a strong connection form. Also we obtain an explicit formula for a strong connection under equivariant projective conditions or under coseparability conditions.

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References

  1. Kreimer, H. F., Takeuchi, H. F.: Hopf algebras and Galois extensions of an algebra. Indiana Univ. Math. J., 30, 675–691 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  2. Brzeziński, T., Majid, S.: Coalgebra bundles. Comm. Math. Phys., 191, 467–492 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  3. Brzeziński, T., Hajac, P. M.: Coalgebra extensions and algebra coextensions of Galois type. Comm. Algebra, 27, 1347–1367 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  4. Brzeziński, T.: The structure of corings, induction functors, Maschke-type theorem, and Frobenius and Galois-type properties. Alg. Rep. Theory, 5, 389–410 (2002)

    Article  MATH  Google Scholar 

  5. Brzeziński, T., Turner, R. B., Wrightson, A. P.: The structure of weak coalgebra-Galois extensions. Comm. Algebra, 34, 1489–1519 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Caenepeel, S., De Groot, E.: Galois theory for weak Hopf algebras. Rev. Roumaine Math. Pures Appl., 52, 51–76 (2007)

    Google Scholar 

  7. Alonso Álvarez, J. N., Fernández Vilaboa, J. M., González Rodríguez, R., et al.: Weak C-cleft extensions and weak Galois extensions. J. Algebra, 299, 276–293 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Hajac, P. M.: Strong connections on quantum principal bundles. Comm. Math. Phys., 182, 579–617 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  9. Böhm, G., Brzeziński, T.: Strong connections and the relative Chern-Galois Character for corings. Int. Math. Res. Notices, 42, 2579–2625 (2005)

    Article  Google Scholar 

  10. Alonso Álvarez, J. N., Fernández Vilaboa, J. M., González Rodríguez, R., et al.: A characterization of projective weak Galois extensions. Israel J. Math., 174, 161–178 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Beggs, E. J., Brzeziński, T.: An explicit formula for a strong connection. Appl. Cat. Str., 16, 57–63 (2008)

    Article  MATH  Google Scholar 

  12. Caenepeel, S., De Groot, E.: Modules over weak entwining structures. AMS Contemp. Math., 206, 31–54 (2000)

    Article  Google Scholar 

  13. Brzeziński, T.: On modules associated to coalgebra Galois extensions. J. Algebra, 215, 290–317 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  14. Schauenburg, P.: Turning monoidal categories into strict ones. New York J. Math., 202, 257–265 (2001)

    MathSciNet  Google Scholar 

  15. Böhm, G.: Internal bialgreboids, entwining structures and corings. AMS Contemp. Math., 376, 207–226 (2005)

    Article  Google Scholar 

  16. Alonso Álvarez, J. N., Fernández Vilaboa, J. M., González Rodríguez, R., et al.: Invertible weak entwining structures and weak C-cleft extensions. Appl. Cat. Str., 14, 411–419 (2006)

    Article  MATH  Google Scholar 

  17. Schauenburg, P., Schneider, H. J.: On generalized Hopf Galois extensions. J. Algebra, 202, 168–194 (2005)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Vigo, Campus Universitario Lagoas-Marcosende, E-36280, Vigo, Spain

    J. N. Alonso Álvarez

  2. Departamento de Álxebra, Universidad de Santiago de Compostela, E-15771, Santiago de Compostela, Spain

    J. M. Fernández Vilaboa

  3. Departamento de Matemática Aplicada II, Universidad de Vigo, Campus Universitario Lagoas-Marcosende, E-36310, Vigo, Spain

    R. González Rodríguez

Authors
  1. J. N. Alonso Álvarez
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  2. J. M. Fernández Vilaboa
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  3. R. González Rodríguez
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Corresponding author

Correspondence to R. González Rodríguez.

Additional information

Supported by Ministerio de Educación, Xunta de Galicia and by FEDER (Grant Nos. MTM2010-15634, MTM2009-14464-C02-01, PGIDT07PXB322079PR)

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Alonso Álvarez, J.N., Fernández Vilaboa, J.M. & González Rodríguez, R. Strong connections and invertible weak entwining structures. Acta. Math. Sin.-English Ser. 28, 1443–1460 (2012). https://doi.org/10.1007/s10114-012-0088-1

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  • DOI: https://doi.org/10.1007/s10114-012-0088-1

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