Groupoid equivalence and the associated iterated crossed product

Jonathan Henry Brown, Geoff Goehle, Dana P. Williams

Research output: Contribution to journalArticle

Abstract

Given groupoids G and H and a (G, H)-equivalence X we may form the transformation groupoid G ⋉ X ⋊ H. Given a separable groupoid dynamical system (A, G ⋉ X ⋊ H, ω) we may restrict ω to an action of G ⋉ X on A and form the crossed product A ⋊ G ⋉ X. We show that there is an action of H on A ⋊ G ⋉ X and that the iterated crossed product (A ⋊ G ⋉ X) ⋊H is naturally isomorphic to the crossed product A ⋊ (G ⋉ X ⋊ H).

Original languageEnglish (US)
Pages (from-to)153-175
Number of pages23
JournalHouston Journal of Mathematics
Volume41
Issue number1
StatePublished - Jan 1 2015

Fingerprint

Groupoid
Crossed Product
Equivalence
Groupoids
Isomorphic
Dynamical system

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Brown, Jonathan Henry ; Goehle, Geoff ; Williams, Dana P. / Groupoid equivalence and the associated iterated crossed product. In: Houston Journal of Mathematics. 2015 ; Vol. 41, No. 1. pp. 153-175.
@article{6a6a25b39a11429ab00fba55ee9c2357,
title = "Groupoid equivalence and the associated iterated crossed product",
abstract = "Given groupoids G and H and a (G, H)-equivalence X we may form the transformation groupoid G ⋉ X ⋊ H. Given a separable groupoid dynamical system (A, G ⋉ X ⋊ H, ω) we may restrict ω to an action of G ⋉ X on A and form the crossed product A ⋊ G ⋉ X. We show that there is an action of H on A ⋊ G ⋉ X and that the iterated crossed product (A ⋊ G ⋉ X) ⋊H is naturally isomorphic to the crossed product A ⋊ (G ⋉ X ⋊ H).",
author = "Brown, {Jonathan Henry} and Geoff Goehle and Williams, {Dana P.}",
year = "2015",
month = "1",
day = "1",
language = "English (US)",
volume = "41",
pages = "153--175",
journal = "Houston Journal of Mathematics",
issn = "0362-1588",
publisher = "University of Houston",
number = "1",

}

Groupoid equivalence and the associated iterated crossed product. / Brown, Jonathan Henry; Goehle, Geoff; Williams, Dana P.

In: Houston Journal of Mathematics, Vol. 41, No. 1, 01.01.2015, p. 153-175.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Groupoid equivalence and the associated iterated crossed product

AU - Brown, Jonathan Henry

AU - Goehle, Geoff

AU - Williams, Dana P.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Given groupoids G and H and a (G, H)-equivalence X we may form the transformation groupoid G ⋉ X ⋊ H. Given a separable groupoid dynamical system (A, G ⋉ X ⋊ H, ω) we may restrict ω to an action of G ⋉ X on A and form the crossed product A ⋊ G ⋉ X. We show that there is an action of H on A ⋊ G ⋉ X and that the iterated crossed product (A ⋊ G ⋉ X) ⋊H is naturally isomorphic to the crossed product A ⋊ (G ⋉ X ⋊ H).

AB - Given groupoids G and H and a (G, H)-equivalence X we may form the transformation groupoid G ⋉ X ⋊ H. Given a separable groupoid dynamical system (A, G ⋉ X ⋊ H, ω) we may restrict ω to an action of G ⋉ X on A and form the crossed product A ⋊ G ⋉ X. We show that there is an action of H on A ⋊ G ⋉ X and that the iterated crossed product (A ⋊ G ⋉ X) ⋊H is naturally isomorphic to the crossed product A ⋊ (G ⋉ X ⋊ H).

UR - http://www.scopus.com/inward/record.url?scp=84929167445&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84929167445&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84929167445

VL - 41

SP - 153

EP - 175

JO - Houston Journal of Mathematics

JF - Houston Journal of Mathematics

SN - 0362-1588

IS - 1

ER -