Advertisement

A Categorical Proof of a Useful Result

  • A. Ardizzoni
  • C. Menini
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

We give a categorical proof of the following equality
$$ \bigcap\limits_{i = 0}^n {\left( {V \otimes V_{n - i} + V_i \otimes V} \right) = } \sum\limits_{i = 1}^n {V_i \otimes V_{n + 1 - i} } $$
which holds for any chain {0} = V 0V 1V 2 ⊆ ... of subspaces of space V.

Keywords

Monoidal categories abelian categories colimits 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AM]
    A. Ardizzoni and C. Menini, Braided Bialgebras of Type One: Applications, submitted. (arXiv:0704.2106v1)Google Scholar
  2. [Ar]
    A. Ardizzoni, Wedge Products and Cotensor Coalgebras in Monoidal Categories, Algebr. Represent. Theory, to appear. (arXiv:math.CT/0602016)Google Scholar
  3. [Ka]
    C. Kassel, Quantum Groups, Graduate Text in Mathematics 155, Springer, 1995.Google Scholar
  4. [Maj]
    S. Majid, Foundations of quantum group theory, Cambridge University Press, 1995.Google Scholar
  5. [Mo]
    S. Montgomery, Hopf Algebras and their actions on rings, CMBS Regional Conference Series in Mathematics 82, 1993.Google Scholar
  6. [Sw]
    M. Sweedler, Hopf Algebras, Benjamin, New York, 1969.Google Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • A. Ardizzoni
    • 1
  • C. Menini
    • 1
  1. 1.Department of MathematicsUniversity of FerraraFerraraItaly

Personalised recommendations