https://nova.newcastle.edu.au/vital/access/ /manager/Index en-au 5 https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:38290 n(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}→F_p((t))→G→F_p((t))→{0}of the additive group of the field of formal Laurent series over F_p=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.]]> Thu 26 Aug 2021 14:13:11 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:38494 Mon 11 Oct 2021 14:41:00 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:36785 α of a voltage digraph, which has arcs weighted by the elements of a group. As a main result, when the involved group is Abelian, we completely determine the spectrum of Γ^α. As some examples of our technique, we study some basic properties of the Alegre digraph, and completely characterize the spectrum of a new family of digraphs, which contains the generalized Petersen graphs, and the Hoffman-Singleton graph.]]> Mon 06 Jul 2020 09:53:43 AEST ]]>