Journal of Noncommutative Geometry

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Volume 12, Issue 1, 2018, pp. 331–368
DOI: 10.4171/JNCG/278

Published online: 2018-03-23

Graded twisting of comodule algebras and module categories

Julien Bichon[1], Sergey Neshveyev[2] and Makoto Yamashita[3]

(1) Université Clermont Auvergne, Aubière, France
(2) University of Oslo, Norway
(3) Ochanomizu University, Tokyo, Japan

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 $G\subset\mathrm {SL}_{-1}(2)$ on $K_{-1}[x,y]$ and show that in most cases the corresponding invariant rings $K_{-1}[x,y]^G$ are invariant rings $K[x,y]^{G'}$ for the action of a classical subgroup $G'\subset \mathrm {SL}(2)$. 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.

Keywords: Hopf algebras, comodule algebras, coinvariants, monoidal categories, module categories over monoidal categories, Poisson boundary

Bichon Julien, Neshveyev Sergey, Yamashita Makoto: Graded twisting of comodule algebras and module categories. J. Noncommut. Geom. 12 (2018), 331-368. doi: 10.4171/JNCG/278