Decompositions of locally compact contraction groups, series and extensions.

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 α 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 / p Z 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. [ABSTRACT FROM AUTHOR]