Comptes Rendus
Research article - Functional analysis
A note on quantum subgroups of free quantum groups
Mao Hoshino1; Kan Kitamura1
1Graduate School of Mathematical Sciences, the University of Tokyo, 3-8-1 Komaba Meguro-ku Tokyo 153-8914, Japan
Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1327-1330

In this short note, quantum subgroups in finite free products of the Pontryagin duals of free unitary quantum groups are classified. They correspond to pairs of a subgroup Γ and a subset S of the free group 𝔽 n such that S is Γ-invariant, containing Γ, and connected in the Cayley graph of 𝔽 n .

Dans cette courte note, les sous-groupes quantiques dans les produits libres finis des duaux de Pontryagin des groupes quantiques unitaires libres sont classifiés. Ils correspondent à des paires formées d’un sous-groupe Γ et d’un sous-ensemble S du groupe libre 𝔽 n tel que S est Γ-invariant, contenant Γ, et connexe dans le graphe de Cayley de 𝔽 n .

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DOI: 10.5802/crmath.641
Classification: 46L67, 05C25
Keywords: free unitary quantum group, quantum subgroup, Cayley graph
Mots-clés : groupe quantique unitaire libéré, sous-groupe quantique, graphe de Cayley

Mao Hoshino  1 ; Kan Kitamura  1

1 Graduate School of Mathematical Sciences, the University of Tokyo, 3-8-1 Komaba Meguro-ku Tokyo 153-8914, Japan
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Mao Hoshino; Kan Kitamura. A note on quantum subgroups of free quantum groups. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1327-1330. doi: 10.5802/crmath.641

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