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Twisting algebras using non-commutative torsors: explicit computations

Mathematische Zeitschrift volume 271, pages789–818(2012)Cite this article

Abstract

Non-commutative torsors (equivalently, two-cocycles) for a Hopf algebra can be used to twist comodule algebras. We prove a theorem that affords a presentation by generators and relations for the algebras obtained by such twisting. We give a number of examples, including new constructions of the quantum affine spaces and the quantum tori.

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Affiliations

  1. Institut de Recherche Mathématique Avancée, Université de Strasbourg & CNRS, 7 Rue René Descartes, 67084, Strasbourg Cedex, France

    Pierre Guillot & Christian Kassel

  2. Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571, Japan

    Akira Masuoka

Authors
  1. Pierre Guillot
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  2. Christian Kassel
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  3. Akira Masuoka
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Correspondence to Christian Kassel.

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Guillot, P., Kassel, C. & Masuoka, A. Twisting algebras using non-commutative torsors: explicit computations. Math. Z. 271, 789–818 (2012). https://doi.org/10.1007/s00209-011-0891-x

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Keywords

  • Hopf Algebra
  • Braided Group
  • Monoidal Category
  • Module Algebra
  • Presentation Theorem