Universal overgroup

Arnal, Didier; Selmi, Mohamed; Zergane, Amel

doi:10.1016/j.geomphys.2010.09.015

Cited by 3 publications

(1 citation statement)

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“…And it turns out that the key to reducing the study of Ψ G from topological groups to Lie groups is the amenability. Additional motivation for us is the study of separation properties of unitary representations in terms of suitable moment sets, which we plan to extend from Lie groups (see [ASZ11] and [Ze11]) to more general topological groups, using the methods developed here and the moment sets introduced in [BNi15].…”

Section: Introductionmentioning

confidence: 99%

Amenability and representation theory of pro-Lie groups

Beltiţă

Zergane

2016

Math. Z.

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Abstract. We develop a semigroup approach to representation theory for pro-Lie groups satisfying suitable amenability conditions. As an application of our approach, we establish a one-to-one correspondence between equivalence classes of unitary irreducible representations and coadjoint orbits for a class of pro-Lie groups including all connected locally compact nilpotent groups and arbitrary infinite direct products of nilpotent Lie groups. The usual C * -algebraic approach to group representation theory positivey breaks down for infinite direct products of non-compact locally compact groups, hence the description of their unitary duals in terms of coadjoint orbits is particularly important whenever it is available, being the only description known so far.

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Section: Introductionmentioning

confidence: 99%