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Tannakian duality for affine homogeneous spaces

  Published:2018-02-28
 Printed: Sep 2018
  • Teodor Banica,
    Department of Mathematics, University of Cergy-Pontoise , F-95000 Cergy-Pontoise, France
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Abstract

Associated to any closed quantum subgroup $G\subset U_N^+$ and any index set $I\subset\{1,\dots,N\}$ is a certain homogeneous space $X_{G,I}\subset S^{N-1}_{\mathbb C,+}$, called affine homogeneous space. We discuss here the abstract axiomatization of the algebraic manifolds $X\subset S^{N-1}_{\mathbb C,+}$ which can appear in this way, by using Tannakian duality methods.
Keywords: quantum isometry, noncommutative manifold quantum isometry, noncommutative manifold
MSC Classifications: 46L65, 46L89 show english descriptions Quantizations, deformations
Other ``noncommutative'' mathematics based on $C^*$-algebra theory [See also 58B32, 58B34, 58J22]
46L65 - Quantizations, deformations
46L89 - Other ``noncommutative'' mathematics based on $C^*$-algebra theory [See also 58B32, 58B34, 58J22]
 

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