Given a closed subgroup which is homogeneous, in the sense that we have , the corresponding Tannakian category C must satisfy . Based on this observation, we construct a certain integer , that we call the easiness level of G. The value corresponds to the case where G is easy, and we explore here, with some theory and examples, the case . As a main application, we show that and other liberation inclusions, known to be maximal in the easy setting, remain maximal at the easiness level as well.
I would like to thank J. Bichon, B. Collins, and S. Curran for many discussions on maximality questions over the last few years. Thanks also go to Poulette.
Teo Banica. "Homogeneous quantum groups and their easiness level." Kyoto J. Math. 61 (1) 171 - 205, April 2021. https://doi.org/10.1215/21562261-2019-0077