Coactions on C∗ -Algebras and Universal Properties

Erik Bédos; S. Kaliszewski; John Quigg; Jonathan Turk

doi:10.1007/s10485-023-09741-0

Coactions on C^∗ -Algebras and Universal Properties

Erik Bédos, S. Kaliszewski, John Quigg, Jonathan Turk

Mathematical and Statistical Sciences, School of (SoMSS)

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

Abstract

It is well-known that the maximalization of a coaction of a locally compact group on a C*-algebra enjoys a universal property. We show how this important property can be deduced from a categorical framework by exploiting certain properties of the maximalization functor for coactions. We also provide a dual proof for the universal property of normalization of coactions.

Original language	English (US)
Article number	36
Journal	Applied Categorical Structures
Volume	31
Issue number	5
DOIs	https://doi.org/10.1007/s10485-023-09741-0
State	Published - Oct 2023

Keywords

Action
Coaction
Maximalization
Universal property

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science
Algebra and Number Theory

Access to Document

10.1007/s10485-023-09741-0

Cite this

@article{44c2c6ae647d4090a0eb3bcf644f972b,

title = "Coactions on C∗ -Algebras and Universal Properties",

abstract = "It is well-known that the maximalization of a coaction of a locally compact group on a C*-algebra enjoys a universal property. We show how this important property can be deduced from a categorical framework by exploiting certain properties of the maximalization functor for coactions. We also provide a dual proof for the universal property of normalization of coactions.",

keywords = "Action, Coaction, Maximalization, Universal property",

author = "Erik B{\'e}dos and S. Kaliszewski and John Quigg and Jonathan Turk",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer Nature B.V.",

year = "2023",

month = oct,

doi = "10.1007/s10485-023-09741-0",

language = "English (US)",

volume = "31",

journal = "Applied Categorical Structures",

issn = "0927-2852",

publisher = "Springer Netherlands",

number = "5",

}

TY - JOUR

T1 - Coactions on C∗ -Algebras and Universal Properties

AU - Bédos, Erik

AU - Kaliszewski, S.

AU - Quigg, John

AU - Turk, Jonathan

PY - 2023/10

Y1 - 2023/10

N2 - It is well-known that the maximalization of a coaction of a locally compact group on a C*-algebra enjoys a universal property. We show how this important property can be deduced from a categorical framework by exploiting certain properties of the maximalization functor for coactions. We also provide a dual proof for the universal property of normalization of coactions.

AB - It is well-known that the maximalization of a coaction of a locally compact group on a C*-algebra enjoys a universal property. We show how this important property can be deduced from a categorical framework by exploiting certain properties of the maximalization functor for coactions. We also provide a dual proof for the universal property of normalization of coactions.

KW - Action

KW - Coaction

KW - Maximalization

KW - Universal property

UR - http://www.scopus.com/inward/record.url?scp=85170243276&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85170243276&partnerID=8YFLogxK

U2 - 10.1007/s10485-023-09741-0

DO - 10.1007/s10485-023-09741-0

M3 - Article

SN - 0927-2852

VL - 31

JO - Applied Categorical Structures

JF - Applied Categorical Structures

IS - 5

M1 - 36

ER -