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^*

^*Corresponding author for this work

School of Mathematical Sciences

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

3 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	1053-1084
Number of pages	32
Journal	Acta Mathematica Sinica, English Series
Volume	39
Issue number	6
DOIs	https://doi.org/10.1007/s10114-023-1536-9
State	Published - Jun 2023

Keywords

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

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10.1007/s10114-023-1536-9

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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.",

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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.",

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

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AU - Chen, Xiao Yu

AU - Hu, Nai Hong

AU - Wang, Xiu Ling

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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

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M3 - 文章

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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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Keywords

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