Abstract

WILSON, Mitsuru. Connes-Landi spheres are homogeneous spaces. Rev.colomb.mat. [online]. 2019, vol.53, suppl.1, pp.257-271.  Epub Mar 24, 2020. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v53nsupl.84099.

In this paper, we review some recent developments of compact quantum groups that arise as θ-deformations of compact Lie groups of rank at least two. A θ-deformation is merely a 2-cocycle deformation using an action of a torus of dimension higher than 2. Using the formula (Lemma 5.3) developed in [11], we derive the noncommutative 7-sphere in the sense of Connes and Landi [3] as the fixed-point subalgebra.

Keywords : Noncommutative geometry; quantum homogeneous space; compact quantum group; Connes-Landi deformation; θ-deformation.

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