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

Naihong Hu; Xiao Xu

doi:10.1016/j.bulsci.2025.103738

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

Naihong Hu^*
, Xiao Xu

^*Corresponding author for this work

School of Mathematical Sciences

East China Normal University

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Article number	103738
Journal	Bulletin des Sciences Mathematiques
Volume	206
DOIs	https://doi.org/10.1016/j.bulsci.2025.103738
State	Published - Jan 2026

Keywords

Exotic small quantum groups
Isomorphism reduction theorem
Lusztig small quantum groups
Restricted two-parameter quantum group

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10.1016/j.bulsci.2025.103738

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abstract = "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.",

keywords = "Exotic small quantum groups, Isomorphism reduction theorem, Lusztig small quantum groups, Restricted two-parameter quantum group",

author = "Naihong Hu and Xiao Xu",

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AB - 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.

KW - Exotic small quantum groups

KW - Isomorphism reduction theorem

KW - Lusztig small quantum groups

KW - Restricted two-parameter quantum group

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DO - 10.1016/j.bulsci.2025.103738

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JO - Bulletin des Sciences Mathematiques

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

Abstract

Keywords

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