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The character algebra for module categories over Hopf algebras

Volume 165 / 2021

Noelia Bortolussi, Martín Mombelli Colloquium Mathematicum 165 (2021), 171-197 MSC: 18D20, 16T05. DOI: 10.4064/cm8170-5-2020 Published online: 17 December 2020

Abstract

Given a finite-dimensional Hopf algebra $H$ and an exact indecomposable module category $\mathcal M $ over $\operatorname{Rep} (H)$, we explicitly compute the adjoint algebra $\mathcal A _\mathcal M $ as an object in the category of Yetter–Drinfeld modules over $H$, and the space of class functions ${\rm CF} (\mathcal M )$ associated to $\mathcal M $, as introduced by K. Shimizu (2020). We use our construction to describe these algebras when $H$ is a group algebra and a dual group algebra. This result allows us to compute the adjoint algebra for certain group-theoretical fusion categories.

Authors

  • Noelia BortolussiFacultad de Matemática, Astronomía y Física
    Universidad Nacional de Córdoba
    CIEM – CONICET
    Medina Allende s/n
    (5000) Ciudad Universitaria
    Córdoba, Argentina
    e-mail
    e-mail
  • Martín MombelliFacultad de Matemática, Astronomía y Física
    Universidad Nacional de Córdoba
    CIEM – CONICET
    Medina Allende s/n
    (5000) Ciudad Universitaria
    Córdoba, Argentina
    https://www.famaf.unc.edu.ar/~mombelli
    e-mail
    e-mail

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