Graded twisting of comodule algebras and module categories

  • Julien Bichon

    Université Clermont Auvergne, Aubière, France
  • Sergey Neshveyev

    University of Oslo, Norway
  • Makoto Yamashita

    Ochanomizu University, Tokyo, Japan
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Abstract

Continuing our previous work on graded twisting of Hopf algebras and monoidal categories, we introduce a graded twisting construction for equivariant comodule algebras and module categories. As an example we study actions of quantum subgroups of GSL1(2)G\subset\mathrm {SL}_{-1}(2) on K1[x,y]K_{-1}[x,y] and show that in most cases the corresponding invariant rings K1[x,y]GK_{-1}[x,y]^G are invariant rings K[x,y]GK[x,y]^{G'} for the action of a classical subgroup GSL(2)G'\subset \mathrm {SL}(2). As another example we study Poisson boundaries of graded twisted categories and show that under the assumption of weak amenability they are graded twistings of the Poisson boundaries.

Cite this article

Julien Bichon, Sergey Neshveyev, Makoto Yamashita, Graded twisting of comodule algebras and module categories. J. Noncommut. Geom. 12 (2018), no. 1, pp. 331–368

DOI 10.4171/JNCG/278