Graded twisting of comodule algebras and module categories

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

25 pages; v3: final version, to appear in JNCG

References in corpus (3)

• A Characterization of right coideals of quotient type and its application to classification of Poisson boundaries
• Coherence for monoidal $G$-categories and braided $G$-crossed categories
• On the center of a compact group

Cited by in corpus (5)

• L^2-Betti numbers of rigid C*-tensor categories and discrete quantum groups
• Higher l^2-Betti numbers of universal quantum groups
• Cohomological dimensions of universal cosovereign Hopf algebras
• Noncommutative Poisson boundaries and Furstenberg-Hamana boundaries of Drinfeld doubles
• Towards a classification of compact quantum groups of Lie type