---
_id: '34786'
abstract:
- lang: eng
  text: A locally compact contraction group is a pair (G,α), where G is a locally
    compact group and α:G→G an automorphism such that αn(x)→e pointwise as n→∞. We
    show that every surjective, continuous, equivariant homomorphism between locally
    compact contraction groups admits an equivariant continuous global section. As
    a consequence, extensions of locally compact contraction groups with abelian kernel
    can be described by continuous equivariant cohomology. For each prime number p,
    we use 2-cocycles to construct uncountably many pairwise non-isomorphic totally
    disconnected, locally compact contraction groups (G,α) which are central extensions0→Fp((t))→G→Fp((t))→0
    of the additive group of the field of formal Laurent series over Fp=Z/pZ by itself.
    By contrast, there are only countably many locally compact contraction groups
    (up to isomorphism) which are torsion groups and abelian, as follows from a classification
    of the abelian locally compact contraction groups.
article_type: original
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
- first_name: George A.
  full_name: Willis, George A.
  last_name: Willis
citation:
  ama: Glöckner H, Willis GA. Decompositions of locally compact contraction groups,
    series and extensions. <i>Journal of Algebra</i>. 2021;570:164-214. doi:<a href="https://doi.org/10.1016/j.jalgebra.2020.11.007">https://doi.org/10.1016/j.jalgebra.2020.11.007</a>
  apa: Glöckner, H., &#38; Willis, G. A. (2021). Decompositions of locally compact
    contraction groups, series and extensions. <i>Journal of Algebra</i>, <i>570</i>,
    164–214. <a href="https://doi.org/10.1016/j.jalgebra.2020.11.007">https://doi.org/10.1016/j.jalgebra.2020.11.007</a>
  bibtex: '@article{Glöckner_Willis_2021, title={Decompositions of locally compact
    contraction groups, series and extensions}, volume={570}, DOI={<a href="https://doi.org/10.1016/j.jalgebra.2020.11.007">https://doi.org/10.1016/j.jalgebra.2020.11.007</a>},
    journal={Journal of Algebra}, author={Glöckner, Helge and Willis, George A.},
    year={2021}, pages={164–214} }'
  chicago: 'Glöckner, Helge, and George A. Willis. “Decompositions of Locally Compact
    Contraction Groups, Series and Extensions.” <i>Journal of Algebra</i> 570 (2021):
    164–214. <a href="https://doi.org/10.1016/j.jalgebra.2020.11.007">https://doi.org/10.1016/j.jalgebra.2020.11.007</a>.'
  ieee: 'H. Glöckner and G. A. Willis, “Decompositions of locally compact contraction
    groups, series and extensions,” <i>Journal of Algebra</i>, vol. 570, pp. 164–214,
    2021, doi: <a href="https://doi.org/10.1016/j.jalgebra.2020.11.007">https://doi.org/10.1016/j.jalgebra.2020.11.007</a>.'
  mla: Glöckner, Helge, and George A. Willis. “Decompositions of Locally Compact Contraction
    Groups, Series and Extensions.” <i>Journal of Algebra</i>, vol. 570, 2021, pp.
    164–214, doi:<a href="https://doi.org/10.1016/j.jalgebra.2020.11.007">https://doi.org/10.1016/j.jalgebra.2020.11.007</a>.
  short: H. Glöckner, G.A. Willis, Journal of Algebra 570 (2021) 164–214.
date_created: 2022-12-21T18:43:08Z
date_updated: 2022-12-21T18:58:44Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: https://doi.org/10.1016/j.jalgebra.2020.11.007
intvolume: '       570'
keyword:
- Contraction group
- Torsion group
- Extension
- Cocycle
- Section
- Equivariant cohomology
- Abelian group
- Nilpotent group
- Isomorphism types
language:
- iso: eng
page: 164-214
publication: Journal of Algebra
publication_identifier:
  issn:
  - 0021-8693
quality_controlled: '1'
status: public
title: Decompositions of locally compact contraction groups, series and extensions
type: journal_article
user_id: '178'
volume: 570
year: '2021'
...