On amenable and coamenable coideals

  • Benjamin Anderson-Sackaney

    University of Saskatchewan, Saskatoon, Canada
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We study relative amenability and amenability of a right coideal of a discrete quantum group in terms of its group-like projection . We establish a notion of a -left invariant state and use it to characterize relative amenability. We also develop a notion of coamenability of a compact quasi-subgroup that generalizes coamenability of a quotient as defined by Kalantar, Kasprzak, Skalski, and Vergnioux (2022), where is the compact dual of . In particular, we establish that the coamenable compact quasi-subgroups of are in one-to-one correspondence with the idempotent states on the reduced -algebra . We use this work to obtain results for the duality between relative amenability and amenability of coideals in and coamenability of their codual coideals in , making progress towards a question of Kalantar et al.

Cite this article

Benjamin Anderson-Sackaney, On amenable and coamenable coideals. J. Noncommut. Geom. (2023), published online first

DOI 10.4171/JNCG/550