For and a uniform pro- group and its Iwasawa algebras and we show that the natural map has a splitting provided that vanishes. The image of this splitting is described in terms of a generalised norm operator. This result generalises classical work of Coleman for the case . We verify the vanishing condition for certain unipotent compact -adic Lie groups.
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Peter Schneider, Otmar Venjakob, A splitting for <em>K</em><sub>1</sub> of completed group rings. Comment. Math. Helv. 88 (2013), no. 3, pp. 613–642DOI 10.4171/CMH/298