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Article Dans Une Revue Mathematica Scandinavica Année : 2015

A duality of locally compact groups which does not involve the Haar measure

Résumé

We present a simple and intuitive framework for duality of locally compacts groups, which is not based on the Haar measure. This is a map, functorial on a non-degenerate subcategory, on the category of coinvolutive Hopf \cst-algebras, and a similar map on the category of coinvolutive Hopf-von Neumann algebras. In the \cst-version, this functor sends $C_0(G)$ to $C^*(G)$ and vice versa, for every locally compact group $G$. As opposed to preceding approaches, there is an explicit description of commutative and co-commutative algebras in the range of this map (without assumption of being isomorphic to their bidual): these algebras have the form $C_0(G)$ or $C^*(G)$ respectively, where $G$ is a locally compact group. The von Neumann version of the functor puts into duality, in the group case, the enveloping von Neumann algebras of the algebras above: $C_0(G)^{**}$ and $C^*(G)^{**}$.

Dates et versions

hal-03192532 , version 1 (08-04-2021)

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Yulia Kuznetsova. A duality of locally compact groups which does not involve the Haar measure. Mathematica Scandinavica, 2015, 116, pp.250-286. ⟨10.7146/math.scand.a-21162⟩. ⟨hal-03192532⟩
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