{"keyword":["Contraction group","Torsion group","Extension","Cocycle","Section","Equivariant cohomology","Abelian group","Nilpotent group","Isomorphism types"],"doi":"https://doi.org/10.1016/j.jalgebra.2020.11.007","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."}],"volume":570,"status":"public","author":[{"first_name":"Helge","id":"178","full_name":"Glöckner, Helge","last_name":"Glöckner"},{"first_name":"George A.","last_name":"Willis","full_name":"Willis, George A."}],"publication_identifier":{"issn":["0021-8693"]},"_id":"34786","intvolume":"       570","year":"2021","page":"164-214","type":"journal_article","publication":"Journal of Algebra","date_created":"2022-12-21T18:43:08Z","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"citation":{"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>.","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>","short":"H. Glöckner, G.A. Willis, Journal of Algebra 570 (2021) 164–214.","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>.","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>","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>."},"user_id":"178","article_type":"original","date_updated":"2022-12-21T18:58:44Z","language":[{"iso":"eng"}],"quality_controlled":"1","title":"Decompositions of locally compact contraction groups, series and extensions"}