A remark on the Hochschild dimension of liberated quantum groups

Tomasz Brzeziński; Ulrich Krähmer; Réamonn Ó Buachalla; Karen R. Strung

A remark on the Hochschild dimension of liberated quantum groups

Quantum Algebra 2024-01-26 v2 K-Theory and Homology

Authors: Tomasz Brzeziński , Ulrich Krähmer , Réamonn Ó Buachalla , Karen R. Strung

Abstract

Let $A$ be a Hopf algebra equipped with a projection onto the coordinate Hopf algebra $\mathcal{O}(G)$ of a semisimple algebraic group $G$ . It is shown that if $A$ admits a suitably non-degenerate comodule $V$ and the induced $G$ -module structure of $V$ is non-trivial, then the third Hochschild homology group of $A$ is non-trivial.

Keywords

hopf algebra semisimple algebraic group comodule hochschild homology liberated quantum groups

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@article{arxiv.2211.01996,
  title  = {A remark on the Hochschild dimension of liberated quantum groups},
  author = {Tomasz Brzeziński and Ulrich Krähmer and Réamonn Ó Buachalla and Karen R. Strung},
  journal= {arXiv preprint arXiv:2211.01996},
  year   = {2024}
}

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to appear in J. Noncomm. Geom

A remark on the Hochschild dimension of liberated quantum groups

Abstract

Keywords

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