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Normal Hopf subalgebras in cocycle deformations of finite groups

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Abstract

Let G be a finite group and let π : G → G′ be a surjective group homomorphism. Consider the cocycle deformation L = H σ of the Hopf algebra H = k G of k-valued linear functions on G, with respect to some convolution invertible 2-cocycle σ. The (normal) Hopf subalgebra \(k^{G'} \subseteq k^{G}\) corresponds to a Hopf subalgebra \(L' \subseteq L\). Our main result is an explicit necessary and sufficient condition for the normality of L′ in L.

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Authors and Affiliations

  1. Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, CIEM–CONICET, (5000) Ciudad Universitaria, Córdoba, Argentina

    César Galindo & Sonia Natale

Authors
  1. César Galindo
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  2. Sonia Natale
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Correspondence to Sonia Natale.

Additional information

This work was partially supported by CONICET, Fundación Antorchas, Agencia Córdoba Ciencia, ANPCyT and Secyt (UNC).

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Galindo, C., Natale, S. Normal Hopf subalgebras in cocycle deformations of finite groups. manuscripta math. 125, 501–514 (2008). https://doi.org/10.1007/s00229-007-0156-5

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  • DOI: https://doi.org/10.1007/s00229-007-0156-5

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