Convex PBW-type Lyndon Bases and Restricted Two-parameter Quantum Group of Type F 4

Xiao Yu Chen; Nai Hong Hu; Xiu Ling Wang

doi:10.1007/s10114-023-1536-9

Convex PBW-type Lyndon Bases and Restricted Two-parameter Quantum Group of Type F ₄

Xiao Yu Chen
, Nai Hong Hu
, Xiu Ling Wang^*

^*此作品的通讯作者

数学科学学院

Shanghai Normal University
Nankai University

科研成果: 期刊稿件 › 文章 › 同行评审

4 引用（Scopus）

摘要

The convex PBW-type Lyndon basis for two-parameter quantum group U_r,s (F₄)is given. Assume that rs⁻¹ is a primitive ℓ-th root of unity with ℓ odd, then the restricted quantum group u_r_,_s(F₄) as a quotient of U_r,s(F₄) is pointed, and of a Drinfel’d double structure under a certain condition. All of Hopf isomorphisms of u_r_,_s(F₄) are determined, and the necessary and sufficient condition for u_r_,_s(F₄) to be a ribbon Hopf algebra is singled out by describing the left and right integrals.

源语言	英语
页（从-至）	1053-1084
页数	32
期刊	Acta Mathematica Sinica, English Series
卷	39
期	6
DOI	https://doi.org/10.1007/s10114-023-1536-9
出版状态	已出版 - 6月 2023

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title = "Convex PBW-type Lyndon Bases and Restricted Two-parameter Quantum Group of Type F 4",

abstract = "The convex PBW-type Lyndon basis for two-parameter quantum group Ur,s (F4)is given. Assume that rs−1 is a primitive ℓ-th root of unity with ℓ odd, then the restricted quantum group ur,s(F4) as a quotient of Ur,s(F4) is pointed, and of a Drinfel{\textquoteright}d double structure under a certain condition. All of Hopf isomorphisms of ur,s(F4) are determined, and the necessary and sufficient condition for ur,s(F4) to be a ribbon Hopf algebra is singled out by describing the left and right integrals.",

keywords = "17B35, 17B37, 81R50, Convex PBW-type Lyndon basis, integrals, restricted 2-parameter quantum groups, ribbon Hopf algebra",

author = "Chen, \{Xiao Yu\} and Hu, \{Nai Hong\} and Wang, \{Xiu Ling\}",

note = "Publisher Copyright: {\textcopyright} 2023, Springer-Verlag GmbH Germany \& The Editorial Office of AMS.",

year = "2023",

month = jun,

doi = "10.1007/s10114-023-1536-9",

language = "英语",

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T1 - Convex PBW-type Lyndon Bases and Restricted Two-parameter Quantum Group of Type F 4

AU - Chen, Xiao Yu

AU - Hu, Nai Hong

AU - Wang, Xiu Ling

PY - 2023/6

Y1 - 2023/6

N2 - The convex PBW-type Lyndon basis for two-parameter quantum group Ur,s (F4)is given. Assume that rs−1 is a primitive ℓ-th root of unity with ℓ odd, then the restricted quantum group ur,s(F4) as a quotient of Ur,s(F4) is pointed, and of a Drinfel’d double structure under a certain condition. All of Hopf isomorphisms of ur,s(F4) are determined, and the necessary and sufficient condition for ur,s(F4) to be a ribbon Hopf algebra is singled out by describing the left and right integrals.

AB - The convex PBW-type Lyndon basis for two-parameter quantum group Ur,s (F4)is given. Assume that rs−1 is a primitive ℓ-th root of unity with ℓ odd, then the restricted quantum group ur,s(F4) as a quotient of Ur,s(F4) is pointed, and of a Drinfel’d double structure under a certain condition. All of Hopf isomorphisms of ur,s(F4) are determined, and the necessary and sufficient condition for ur,s(F4) to be a ribbon Hopf algebra is singled out by describing the left and right integrals.

KW - 17B35

KW - 17B37

KW - 81R50

KW - Convex PBW-type Lyndon basis

KW - integrals

KW - restricted 2-parameter quantum groups

KW - ribbon Hopf algebra

UR - https://www.scopus.com/pages/publications/85153040464

U2 - 10.1007/s10114-023-1536-9

DO - 10.1007/s10114-023-1536-9

M3 - 文章

AN - SCOPUS:85153040464

SN - 1439-8516

VL - 39

SP - 1053

EP - 1084

JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 6

ER -

Convex PBW-type Lyndon Bases and Restricted Two-parameter Quantum Group of Type F 4

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Convex PBW-type Lyndon Bases and Restricted Two-parameter Quantum Group of Type F ₄