Multiplier representations of abelian groups

Principe d’incertitude qualitatif pour les groupes de Lie nilpotents

“…En utilisant [6], nous définissons la transformée de Fourierà valeurs opérateurs. Soit F ∈ G * , il existe une suite de sous-algèbres de Lie G j de G telles que :…”

Generalized non-commutative tori

“…The multiplier ω determines a subgroup S ω of G, called its symmetry group, and ω is called totally skew if the symmetry group S ω is trivial; the torus A ω is then called completely irrational (see [1]). It was shown in [1] that if G is a locally compact abelian group and ω is a totally skew multiplier on G, then C In [5], it was shown that two separable C * -algebras A and B are stably isomorphic if and only if they are strongly Morita equivalent, i.e., there exists an A-B-equivalence bimodule defined in [14]. In [4], M. Brabanter constructed an A m/k -C(T 2 )-equivalence bimodule.…”

“…By a change of basis, one can assume that [1,9,13]). This assures us of the existence of such actions α i as in the definition of T k in the abstract.…”

A Plancherel formula for idyllic nilpotent Lie groups

“…That Ps{y) G M+(E) and properties (i) and (ii) follow from Theorem 3.1 and the fact that G orbits are closed in V' (Proposition 3.1(a)). The proof of (iii) and formula (3.13) consists in (1) showing that p o s(xwmRd) is a pseudo-image of xEmv, by p; (2) (3) showing that the orbit measures provided by Bourbaki's theorem are \detM^(s(y))\vs, y The following three lemmas show that the measure p ° s(xwmxxd) on E/G is a pseudo-image of the measure xEmv, on F. Equation (3.14) in Lemma 3.3 would be the disintegration formula (3.13) if we knew that |det dH(y, t)\ = J(y, t) = J(y, 0)mRdxRr a. a. (y, t).…”