- Title
- Decompositions of locally compact contraction groups, series and extensions
- Creator
- Glöckner, Helge; Willis, George A.
- Relation
- Journal of Algebra Vol. 570, Issue 15 March 2021, p. 164-214
- Publisher Link
- http://dx.doi.org/10.1016/j.jalgebra.2020.11.007
- Publisher
- Academic Press
- Resource Type
- journal article
- Date
- 2021
- Description
- 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 extensions{0}→Fp((t))→G→Fp((t))→{0}of the additive group of the field of formal Laurent series over Fp=Z/pZby 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.
- Subject
- contraction group; Torsion group; extension; cocycle; section; equivariant cohomology; Abelian group; Nilpotent group; isomorphism types
- Identifier
- http://hdl.handle.net/1959.13/1425662
- Identifier
- uon:38290
- Identifier
- ISSN:0021-8693
- Language
- eng
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