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Highlights in Lie Algebraic Methods pp 189–203Cite as

Birkhäuser

Hopf Algebras and Frobenius Algebras in Finite Tensor Categories

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Part of the book series: Progress in Mathematics ((PM,volume 295))

Abstract

We discuss algebraic and representation theoretic structures in braided tensor categories \(\mathcal{C}\) which obey certain finiteness conditions. A lot of interesting structure of such a category is encoded in a Hopf algebra \(\mathcal{H}\) in \(\mathcal{C}\). In particular, the Hopf algebra \(\mathcal{H}\) gives rise to representations of the modular group SL(2,ℤ) on various morphism spaces. We also explain how every symmetric special Frobenius algebra in a semisimple modular category provides additional structure related to these representations.

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Acknowledgements

J.F. is partially supported by VR under project no. 621-2009-3343. C.S. is partially supported by the DFG Priority Program 1388 “Representation theory.”

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Authors and Affiliations

  1. Organisationseinheit Mathematik, Bereich Algebra und Zahlentheorie, Universität Hamburg, Bundesstraße 55, 20146, Hamburg, Germany

    Christoph Schweigert

  2. Teoretisk Fysik, Karlstads Universitet, Universitetsgatan 21, 65188, Karlstad, Sweden

    Jürgen Fuchs

Authors
  1. Christoph Schweigert
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  2. Jürgen Fuchs
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Correspondence to Christoph Schweigert .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Weizmann Institute, Rehovot, 76100, Israel

    Anthony Joseph

  2. Department of Mathematics, Univeristy of Haifa, Haifa, 31905, Israel

    Anna Melnikov

  3. School of Engineering and Science, Jacobs University, Bremen, 28759, Germany

    Ivan Penkov

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Schweigert, C., Fuchs, J. (2012). Hopf Algebras and Frobenius Algebras in Finite Tensor Categories. In: Joseph, A., Melnikov, A., Penkov, I. (eds) Highlights in Lie Algebraic Methods. Progress in Mathematics, vol 295. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8274-3_8

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