On positive definiteness over locally compact quantum groups

Volker Runde; Ami Viselter

doi:10.4153/CJM-2015-019-0

On positive definiteness over locally compact quantum groups

Volker Runde, Ami Viselter

Department of Mathematics

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

Abstract

The notion of positive-definite functions over locally compact quantum groups was recently introduced and studied by Daws and Salmi. Based on this work, we generalize various wellknown results about positive-definite functions over groups to the quantum framework. Among these are theorems on "square roots" of positive-definite functions, comparison of various topologies, positive-definite measures and characterizations of amenability, and the separation property with respect to compact quantum subgroups.

Original language	English
Pages (from-to)	1067-1095
Number of pages	29
Journal	Canadian Journal of Mathematics
Volume	68
Issue number	5
DOIs	https://doi.org/10.4153/CJM-2015-019-0
State	Published - Oct 2016

Bibliographical note

Publisher Copyright:
© Canadian Mathematical Society 2016.

Keywords

Bicrossed product
Locally compact quantum group
Non-commutative L-space
Positive-definite function
Positive-definite measure
Separation property

ASJC Scopus subject areas

General Mathematics

Access to Document

10.4153/CJM-2015-019-0

Cite this

@article{b063400e858848899b25c11c0bd1230e,

title = "On positive definiteness over locally compact quantum groups",

abstract = "The notion of positive-definite functions over locally compact quantum groups was recently introduced and studied by Daws and Salmi. Based on this work, we generalize various wellknown results about positive-definite functions over groups to the quantum framework. Among these are theorems on {"}square roots{"} of positive-definite functions, comparison of various topologies, positive-definite measures and characterizations of amenability, and the separation property with respect to compact quantum subgroups.",

keywords = "Bicrossed product, Locally compact quantum group, Non-commutative L-space, Positive-definite function, Positive-definite measure, Separation property",

author = "Volker Runde and Ami Viselter",

note = "Publisher Copyright: {\textcopyright} Canadian Mathematical Society 2016.",

year = "2016",

month = oct,

doi = "10.4153/CJM-2015-019-0",

language = "English",

volume = "68",

pages = "1067--1095",

journal = "Canadian Journal of Mathematics",

issn = "0008-414X",

publisher = "Canadian Mathematical Society",

number = "5",

}

TY - JOUR

T1 - On positive definiteness over locally compact quantum groups

AU - Runde, Volker

AU - Viselter, Ami

N1 - Publisher Copyright: © Canadian Mathematical Society 2016.

PY - 2016/10

Y1 - 2016/10

N2 - The notion of positive-definite functions over locally compact quantum groups was recently introduced and studied by Daws and Salmi. Based on this work, we generalize various wellknown results about positive-definite functions over groups to the quantum framework. Among these are theorems on "square roots" of positive-definite functions, comparison of various topologies, positive-definite measures and characterizations of amenability, and the separation property with respect to compact quantum subgroups.

AB - The notion of positive-definite functions over locally compact quantum groups was recently introduced and studied by Daws and Salmi. Based on this work, we generalize various wellknown results about positive-definite functions over groups to the quantum framework. Among these are theorems on "square roots" of positive-definite functions, comparison of various topologies, positive-definite measures and characterizations of amenability, and the separation property with respect to compact quantum subgroups.

KW - Bicrossed product

KW - Locally compact quantum group

KW - Non-commutative L-space

KW - Positive-definite function

KW - Positive-definite measure

KW - Separation property

UR - http://www.scopus.com/inward/record.url?scp=84983680188&partnerID=8YFLogxK

U2 - 10.4153/CJM-2015-019-0

DO - 10.4153/CJM-2015-019-0

M3 - Article

AN - SCOPUS:84983680188

SN - 0008-414X

VL - 68

SP - 1067

EP - 1095

JO - Canadian Journal of Mathematics

JF - Canadian Journal of Mathematics

IS - 5

ER -

On positive definiteness over locally compact quantum groups

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this