A characterization for discrete quantum group

Ming Liu; Lining Jiang; Guosheng Zhang

doi:10.5269/bspm.v23i1-2.7455

A characterization for discrete quantum group

Ming Liu, Lining Jiang, Guosheng Zhang^*

^*Corresponding author for this work

School of Mathematics and Statistics

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

1 Citation (Scopus)

Abstract

Based on the work of A.Van Daele, E.G.Effros and Z.J.Ruan on mul-tiplier Hopf algerba and discrete quantum group, this paper states that discrete quantum group (A, Δ) is exactly the set {(ω - ⊗)Δ(a)|a ε A; ω 2 A*}, where A* is the space of all reduced functionals on A. Furthermore, this paper characterizes (A, Δ) as an algebraic quantum group with a standard *-operation and a special element z ε A such that (1 ⊗ a)Δ(z) = Δ(z)(a ⊗ 1) (∀a ε A).

Original language	English
Pages (from-to)	41-50
Number of pages	10
Journal	Boletim da Sociedade Paranaense de Matematica
Volume	23
Issue number	1-2
DOIs	https://doi.org/10.5269/bspm.v23i1-2.7455
Publication status	Published - 2005

Keywords

Cointegral
Discrete quantum group
Reduced functional

Access to Document

10.5269/bspm.v23i1-2.7455

Cite this

Liu, M., Jiang, L., & Zhang, G. (2005). A characterization for discrete quantum group. Boletim da Sociedade Paranaense de Matematica, 23(1-2), 41-50. https://doi.org/10.5269/bspm.v23i1-2.7455

@article{1680c21b2341459eaa53472397c3bfd8,

title = "A characterization for discrete quantum group",

abstract = "Based on the work of A.Van Daele, E.G.Effros and Z.J.Ruan on mul-tiplier Hopf algerba and discrete quantum group, this paper states that discrete quantum group (A, Δ) is exactly the set {(ω - ⊗)Δ(a)|a ε A; ω 2 A*}, where A* is the space of all reduced functionals on A. Furthermore, this paper characterizes (A, Δ) as an algebraic quantum group with a standard *-operation and a special element z ε A such that (1 ⊗ a)Δ(z) = Δ(z)(a ⊗ 1) (∀a ε A).",

keywords = "Cointegral, Discrete quantum group, Reduced functional",

author = "Ming Liu and Lining Jiang and Guosheng Zhang",

year = "2005",

doi = "10.5269/bspm.v23i1-2.7455",

language = "English",

volume = "23",

pages = "41--50",

journal = "Boletim da Sociedade Paranaense de Matematica",

issn = "0037-8712",

publisher = "Sociedade Brasileira de Matematica",

number = "1-2",

}

TY - JOUR

T1 - A characterization for discrete quantum group

AU - Liu, Ming

AU - Jiang, Lining

AU - Zhang, Guosheng

PY - 2005

Y1 - 2005

N2 - Based on the work of A.Van Daele, E.G.Effros and Z.J.Ruan on mul-tiplier Hopf algerba and discrete quantum group, this paper states that discrete quantum group (A, Δ) is exactly the set {(ω - ⊗)Δ(a)|a ε A; ω 2 A*}, where A* is the space of all reduced functionals on A. Furthermore, this paper characterizes (A, Δ) as an algebraic quantum group with a standard *-operation and a special element z ε A such that (1 ⊗ a)Δ(z) = Δ(z)(a ⊗ 1) (∀a ε A).

AB - Based on the work of A.Van Daele, E.G.Effros and Z.J.Ruan on mul-tiplier Hopf algerba and discrete quantum group, this paper states that discrete quantum group (A, Δ) is exactly the set {(ω - ⊗)Δ(a)|a ε A; ω 2 A*}, where A* is the space of all reduced functionals on A. Furthermore, this paper characterizes (A, Δ) as an algebraic quantum group with a standard *-operation and a special element z ε A such that (1 ⊗ a)Δ(z) = Δ(z)(a ⊗ 1) (∀a ε A).

KW - Cointegral

KW - Discrete quantum group

KW - Reduced functional

UR - http://www.scopus.com/inward/record.url?scp=84881295765&partnerID=8YFLogxK

U2 - 10.5269/bspm.v23i1-2.7455

DO - 10.5269/bspm.v23i1-2.7455

M3 - Article

AN - SCOPUS:84881295765

SN - 0037-8712

VL - 23

SP - 41

EP - 50

JO - Boletim da Sociedade Paranaense de Matematica

JF - Boletim da Sociedade Paranaense de Matematica

IS - 1-2

ER -

A characterization for discrete quantum group

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this