@article{34786,
  abstract     = {{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.}},
  author       = {{Glöckner, Helge and Willis, George A.}},
  issn         = {{0021-8693}},
  journal      = {{Journal of Algebra}},
  keywords     = {{Contraction group, Torsion group, Extension, Cocycle, Section, Equivariant cohomology, Abelian group, Nilpotent group, Isomorphism types}},
  pages        = {{164--214}},
  title        = {{{Decompositions of locally compact contraction groups, series and extensions}}},
  doi          = {{https://doi.org/10.1016/j.jalgebra.2020.11.007}},
  volume       = {{570}},
  year         = {{2021}},
}