A remark on the Hochschild dimension of liberated quantum groups

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

doi:10.4171/jncg/572

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A remark on the Hochschild dimension of liberated quantum groups

Tomasz Brzeziński
Swansea University, Swansea, UK; University of Białystok, Białystok, Poland
Ulrich Krähmer
Technische Universität Dresden, Dresden, Germany
Réamonn Ó Buachalla
Charles University, Prague, Czech Republic
Karen R. Strung
Czech Academy of Sciences, Prague, Czech Republic

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Abstract

Let $A$ be a Hopf algebra equipped with a projection onto the coordinate Hopf algebra $O (G)$ 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.

Cite this article

Tomasz Brzeziński, Ulrich Krähmer, Réamonn Ó Buachalla, Karen R. Strung, A remark on the Hochschild dimension of liberated quantum groups. J. Noncommut. Geom. (2024), published online first

DOI 10.4171/JNCG/572