On infinitely small orbits

Simply connected nilpotent Lie groups with quasi-standard $C^*$-algebras

“…) and C * (G 5,6 ) are quasi-standard by (i) of the theorem. Next, G 5,2 is 2-step nilpotent with 2-dimensional centre and d(G 5,2 ) = 2, so that by the theorem there is a Glimm ideal in C * (G 5,2 ) which is not primal.…”

“…We now recall from [4] and [6] the definition of the cortex, cor(G), of a locally compact group G. This is the closed subset of G consisting of all those π ∈ G that cannot be separated by open sets from the trivial representation. Clearly, {ker π : π ∈ cor(G)} is contained in the Glimm class [ker 1 G ] of Prim(C * (G)).…”

An approach to the tangential Poisson cohomology based on examples in duals of Lie algebras

“…The same is true for the union Ω of all maximal dimensional coadjoint orbits in g * 4,1 . The computation of the TP-cohomology spaces for g 5,4 , g 6,18 or for all the filiform Lie algebras, studied for instance in [Pe1,Pe2,CG,GK,BLM], leads to the same results as in the g 4,1 -case. Due to these examples, we believe that the TP-cohomology spaces of a regular Poisson manifold M are huge and rather complicated to compute whenever the quotient space of M by the foliation is not Hausdorff.…”

Completely bounded mappings and simplicial complex structure in the primitive ideal space of a $C^*$-algebra

“…However, this property fails for G N with N ≥ 5 (see [6] and [8,Theorem 3.1]). For N ≥ 5, it follows from [12] (see also [8, …”

“…We can establish a variant of Corollary 4.5 for the unitisation of the direct sum, with a somewhat similar proof, and this allows us to show L (A 1 ) = ∞. (ii) Let G N (N ≥ 3) be the 'thread-like' nilpotent Lie groups (see, for example, [12,6,8]). The group G 3 is the continuous Heisenberg group.…”