On primary ideals in group algebras

Ideals with bounded approximate units in L1-algebras of locally compact groups

“…(4) Exploiting an idea of [15], it was shown in [17] that every 2-step nilpotent locally compact group is weakly centrally inductive.…”

Lebesgue type decomposition of subspaces of Fourier-Stieltjes algebras

“…Conversely, if K as in (ii) exists, then, after passing to G/K, we can assume that Z(G) = T. Let χ(z) = z for z ∈ T, and choose π ∈ G such that π|Z(G) ∼ χ. If, in addition, G is 2-step nilpotent, then π ∼ ind G H ϕ, where H is a closed subgroup of G containing Z(G) and ϕ is a G-invariant character of H. In fact, using an idea of [24], this has been shown in [25] for arbitrary 2-step nilpotent locally compact groups. We have to show that H = Z(G).…”

On the support of the conjugation representation for solvable locally compact groups

“…For the converse inclusion we show that 8υρρ(π (g) π) c cor(G) for every element π of G. For this purpose let π any element of , choose λ e Z(G) with 7i|Z(G) ~ λ, and define These definitions yield Η λ /Ζ λ = Z(G/ZJ, that is Η λ /Ζ λ is abelian. [11,Lemma 2] provides the existence of a G-invariant character α e (// λ /Ζ λ ) Λ such that π ~ indj^a. This implies supp(n (χ) π) s (G/// A ) A because of (π (g) π)\Η λ ~ α (g) οι = \ Ηλ .…”