On the ℓ
            2 -Betti numbers of universal quantum groups

David Kyed; Sven  Raum

doi:10.1007/s00208-017-1531-5

On the ℓ ² -Betti numbers of universal quantum groups

David Kyed, Sven Raum

Department of Mathematics and Computer Science

Swiss Federal Institute of Technology in Lausanne

Research output: Contribution to journal › Journal article › Research › peer-review

Abstract

We show that the first ℓ ²-Betti number of the duals of the free unitary quantum groups is one, and that all ℓ ²-Betti numbers vanish for the duals of the quantum automorphism groups of full matrix algebras.

Original language	English
Journal	Mathematische Annalen
Volume	369
Issue number	3-4
Pages (from-to)	957-975
ISSN	0025-5831
DOIs	https://doi.org/10.1007/s00208-017-1531-5
Publication status	Published - 2017

Keywords

Free unitary quantum groups
Quantum automorphism groups
ℓ -Betti numbers

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10.1007/s00208-017-1531-5

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Cite this

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title = "On the ℓ 2 -Betti numbers of universal quantum groups",

abstract = "We show that the first ℓ 2-Betti number of the duals of the free unitary quantum groups is one, and that all ℓ 2-Betti numbers vanish for the duals of the quantum automorphism groups of full matrix algebras.",

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author = "David Kyed and Sven Raum",

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AU - Kyed, David

AU - Raum, Sven

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N2 - We show that the first ℓ 2-Betti number of the duals of the free unitary quantum groups is one, and that all ℓ 2-Betti numbers vanish for the duals of the quantum automorphism groups of full matrix algebras.

AB - We show that the first ℓ 2-Betti number of the duals of the free unitary quantum groups is one, and that all ℓ 2-Betti numbers vanish for the duals of the quantum automorphism groups of full matrix algebras.

KW - Free unitary quantum groups

KW - Quantum automorphism groups

KW - ℓ -Betti numbers

U2 - 10.1007/s00208-017-1531-5

DO - 10.1007/s00208-017-1531-5

M3 - Journal article

SN - 0025-5831

VL - 369

SP - 957

EP - 975

JO - Mathematische Annalen

JF - Mathematische Annalen

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On the ℓ 2 -Betti numbers of universal quantum groups