Skip to main content
Log in

The Tannaka Representation Theorem for Separable Frobenius Functors

  • Published:
Algebras and Representation Theory Aims and scope Submit manuscript

Abstract

A weak bialgebra is known to be a special case of a bialgebroid. In this paper we study the relationship of this fact with the Tannaka theory of bialgebroids as developed in Phùng Hô Hai (Isr J Math 167(1):193–225, 2008). We obtain a Tannaka representation theorem with respect to a separable Frobenius fiber functor.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Day, B., Pastro, C.: A note on Frobenius monoidal functors. N.Y. J. Math. 14, 733–742 (2008)

    MathSciNet  MATH  Google Scholar 

  2. Hai P.H.: Tannaka-Krein duality for Hopf algebroids. Isr. J. Math. 167(1), 193–225 (2008)

    Article  MATH  Google Scholar 

  3. Joyal, A., Street, R.: An introduction to Tannaka duality and quantum groups, Part II of category theory. In: Proceedings, Como 1990, Lecture Notes in Math. vol. 1488, pp. 411–492. Springer, Heidelberg (1991)

    Google Scholar 

  4. Joyal, A., Street, R.: The geometry of tensor calculus I. Adv. Math. 88, 55–112 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  5. McCurdy, M.: Tannaka Reconstruction of Weak Hopf Algebras in Arbitrary Monoidal Categories. (2009). arXiv:0903.0208v1

  6. Schauenburg, P.: Weak Hopf algebras and quantum groupoids. Noncommutative geometry and quantum groups (Warsaw, 2001), pp. 171–188, Banach Center Publ. vol. 61, Polish Acad. Sci., Warsaw (2003)

  7. Street, R.: Quantum groups: a path to current algebra. Australian Mathematical Society Lecture Series, vol. 19. Cambridge University press (2007)

  8. Szlachńyi, K.: Finite quantum groupoids and inclusions of finite type. Fields Inst. Commun. 30, 393–407 (2001)

    Google Scholar 

  9. Szlachányi, K.: Adjointable monoidal functors and quantum groupoids. Lect. Notes Pure Appl. Math. 239, 291–308 (2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dimitri Chikhladze.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chikhladze, D. The Tannaka Representation Theorem for Separable Frobenius Functors. Algebr Represent Theor 15, 1205–1213 (2012). https://doi.org/10.1007/s10468-011-9285-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10468-011-9285-3

Keywords

Mathematics Subject Classifications (2010)

Navigation