Twisting algebras using non-commutative torsors: explicit computations

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• 作者：Pierre Guillot (1) guillot@math.unistra.fr
  Christian Kassel (1) kassel@math.unistra.fr
  Akira Masuoka (2) akira@math.tsukuba.ac.jp
• 刊名：Mathematische Zeitschrift
• 出版年：2012
• 出版时间：August 2012
• 年：2012
• 卷：271
• 期：3-4
• 页码：789-818
• 全文大小：415.5 KB
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• 作者单位：1. Institut de Recherche Math茅matique Avanc茅e, Universit茅 de Strasbourg & CNRS, 7 Rue Ren茅 Descartes, 67084 Strasbourg Cedex, France2. Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571 Japan
• ISSN：1432-1823

文摘

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.