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Medientyp:
E-Artikel
Titel:
Quantum Groups with Partial Commutation Relations
Beteiligte:
Speicher, Roland;
Weber, Moritz
Erschienen:
Indiana University Mathematics Department, 2019
Erschienen in:
Indiana University Mathematics Journal, 68 (2019) 6, Seite 1849-1883
Sprache:
Englisch
ISSN:
0022-2518;
1943-5258
Entstehung:
Anmerkungen:
Beschreibung:
<p>We define noncommutative spheres with partial commutation relations for the coordinates. We investigate the quantum groups acting maximally on them, which yields new quantum versions of the orthogonal group; they are partially commutative in a way such that they do <italic>not</italic> interpolate between the classical and the free quantum versions of the orthogonal group. They contain Bichon’s quantum automorphism groups of graphs as quantum versions of the symmetric group. Those fit, in the sense of distributional symmetries, with Młotkowski’s notion of Λ-freeness (which is a mixture of classical and free independence).</p>