Convex PBW-type Lyndon bases and restricted two-parameter quantum groups of type B

Naihong Hu; Xiuling Wang

doi:10.1016/j.geomphys.2009.11.005

Convex PBW-type Lyndon bases and restricted two-parameter quantum groups of type B

Naihong Hu^*, Xiuling Wang

^*Corresponding author for this work

School of Mathematical Sciences

Nankai University

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

20 Scopus citations

Abstract

We construct convex PBW-type Lyndon bases for two-parameter quantum groups U_{r, s} (s o_{2 n + 1}) with detailed commutation relations. It turns out that under a certain condition, the restricted two-parameter quantum group u_{r, s} (s o_{2 n + 1}) (r, s are roots of unity) is a Drinfel'd double. All Hopf isomorphisms of u_{r, s} (s o_{2 n + 1}), as well as u_{r, s} (s l_n), are determined. Finally, necessary and sufficient conditions for u_{r, s} (s o_{2 n + 1}) to be a ribbon Hopf algebra are singled out by describing the left and right integrals.

Original language	English
Pages (from-to)	430-453
Number of pages	24
Journal	Journal of Geometry and Physics
Volume	60
Issue number	3
DOIs	https://doi.org/10.1016/j.geomphys.2009.11.005
State	Published - Mar 2010

Keywords

Convex PBW-type Lyndon basis
Integrals
Restricted two-parameter quantum groups
Ribbon Hopf algebra

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10.1016/j.geomphys.2009.11.005

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title = "Convex PBW-type Lyndon bases and restricted two-parameter quantum groups of type B",

abstract = "We construct convex PBW-type Lyndon bases for two-parameter quantum groups Ur, s (s o2 n + 1) with detailed commutation relations. It turns out that under a certain condition, the restricted two-parameter quantum group ur, s (s o2 n + 1) (r, s are roots of unity) is a Drinfel'd double. All Hopf isomorphisms of ur, s (s o2 n + 1), as well as ur, s (s ln), are determined. Finally, necessary and sufficient conditions for ur, s (s o2 n + 1) to be a ribbon Hopf algebra are singled out by describing the left and right integrals.",

keywords = "Convex PBW-type Lyndon basis, Integrals, Restricted two-parameter quantum groups, Ribbon Hopf algebra",

author = "Naihong Hu and Xiuling Wang",

year = "2010",

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doi = "10.1016/j.geomphys.2009.11.005",

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pages = "430--453",

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T1 - Convex PBW-type Lyndon bases and restricted two-parameter quantum groups of type B

AU - Hu, Naihong

AU - Wang, Xiuling

PY - 2010/3

Y1 - 2010/3

N2 - We construct convex PBW-type Lyndon bases for two-parameter quantum groups Ur, s (s o2 n + 1) with detailed commutation relations. It turns out that under a certain condition, the restricted two-parameter quantum group ur, s (s o2 n + 1) (r, s are roots of unity) is a Drinfel'd double. All Hopf isomorphisms of ur, s (s o2 n + 1), as well as ur, s (s ln), are determined. Finally, necessary and sufficient conditions for ur, s (s o2 n + 1) to be a ribbon Hopf algebra are singled out by describing the left and right integrals.

AB - We construct convex PBW-type Lyndon bases for two-parameter quantum groups Ur, s (s o2 n + 1) with detailed commutation relations. It turns out that under a certain condition, the restricted two-parameter quantum group ur, s (s o2 n + 1) (r, s are roots of unity) is a Drinfel'd double. All Hopf isomorphisms of ur, s (s o2 n + 1), as well as ur, s (s ln), are determined. Finally, necessary and sufficient conditions for ur, s (s o2 n + 1) to be a ribbon Hopf algebra are singled out by describing the left and right integrals.

KW - Convex PBW-type Lyndon basis

KW - Integrals

KW - Restricted two-parameter quantum groups

KW - Ribbon Hopf algebra

UR - https://www.scopus.com/pages/publications/75749143000

U2 - 10.1016/j.geomphys.2009.11.005

DO - 10.1016/j.geomphys.2009.11.005

M3 - 文章

AN - SCOPUS:75749143000

SN - 0393-0440

VL - 60

SP - 430

EP - 453

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

IS - 3

ER -

Convex PBW-type Lyndon bases and restricted two-parameter quantum groups of type B

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Keywords

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