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${session.getAttribute("locale")}5Decompositions of locally compact contraction groups, series and extensions
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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]]>Limits of contraction groups and the tits core
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ϯ of a totally disconnected locally compact group G is defined as the abstract subgroup generated by the closures of the contraction groups of all its elements. We show that a dense subgroup is normalised by the Tits core if and only if it contains it. It follows that every dense subnormal subgroup contains the Tits core. In particular, if G is topologically simple, then the Tits core is abstractly simple, and when G^{ϯ} is non-trivial, it is the smallest dense normal subgroup. The proofs are based on the fact, of independent interest, that the map which associates to an element the closure of its contraction group is continuous.]]>Sat 24 Mar 2018 08:05:59 AEDT]]>Contraction groups in complete Kac-Moody groups
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Sat 24 Mar 2018 07:43:54 AEDT]]>