Quantum isometries and noncommutative spheres

Abstract

We introduce and study two new examples of noncommutative spheres: the half-liberated sphere, and the free sphere. Together with the usual sphere, these two spheres have the property that the corresponding quantum isometry group is "easy", in the representation theory sense. We present as well some general comments on the axiomatization problem, and on the "untwisted" and "non-easy" case.

16 pages

References in corpus (1)

• Quantum Group of Isometries in Classical and Noncommutative Geometry

Cited by in corpus (12)

• On polynomial integrals over the orthogonal group
• Liberations and twists of real and complex spheres
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• Unitary easy quantum groups: geometric aspects
• Matrix models for noncommutative algebraic manifolds
• Quantum Isometry Groups of Noncommutative Manifolds Obtained by Deformation Using Dual Unitary 2-Cocycles
• Quantum Brownian Motion on noncommutative manifolds: construction, deformation and exit times
• Braided quantum symmetries of graph ${\mathrm{C}}^{\ast }$-algebras
• Noncommutative stable homotopy and stable infinity categories
• Tannaka-Krein reconstruction and ergodic actions of easy quantum groups
• Dequantization via quantum channels
• Quantum symmetries on noncommutative complex spheres with partial commutation relations