Novel isoclasses of one-parameter exotic small quantum groups originating from a two-parameter framework

The classification of one-parameter small quantum groups remains a fascinating open problem. This paper uncovers a novel phenomenon: beyond the Lusztig small quantum groups—equipped with double group-like elements [29]—there exists a plethora of exotic small quantum groups, approximately fivefold more numerous than their standard counterparts, which originate from a two-parameter framework.