# Transformée de Zack pour les groupoides à groupe d’isotropie abélien

## Zak transform for groupoids with abelian isotropy

Ibrahima Toure
Université Félix Houphouët-Boigny
Côte d’Ivoire

Kinvi Kangni
Université Félix Houphouët-Boigny
Côte d’Ivoire

Publié le 12 janvier 2023   DOI : 10.21494/ISTE.OP.2023.0904

### Keywords

Let 𝒢 be a second countable locally compact Hausdorff groupoid with abelian isotropy groups and 𝓛 be a lattice bundle in the isotropy subgroupoid 𝒢 ’ of 𝒢. In this paper, we define a Zak transform on 𝒢 relatively to 𝓛 and study some of its properties. Moreover, we use Zak transform to obtain some characterizations of the cyclic subbundle of the left regular representation of 𝒢 restricted to 𝓛.

Let 𝒢 be a second countable locally compact Hausdorff groupoid with abelian isotropy groups and 𝓛 be a lattice bundle in the isotropy subgroupoid 𝒢 ’ of 𝒢. In this paper, we define a Zak transform on 𝒢 relatively to 𝓛 and study some of its properties. Moreover, we use Zak transform to obtain some characterizations of the cyclic subbundle of the left regular representation of 𝒢 restricted to 𝓛.