Compact open sets in duals and projections inL1-algebras of certain semi-direct product groups

Abstract

The main purpose of this paper is to study projections, that is, self-adjoint idempotents, inL1-algebras of semi-direct productsG= ℝ ⋉ ℝd,d≥ 2. We establish necessary and sufficient conditions for the existence of non-zero projections in terms of the action of ℝ on ℝd. In the cases where such projections exist, we describe minimal ones in detail.