Quantum isometries and noncommutative spheres
Teodor Banica, Debashish Goswami
TL;DR
This paper introduces two new noncommutative spheres, the half-liberated and free spheres, and analyzes their quantum isometry groups, contributing to the understanding of noncommutative geometry and quantum symmetries.
Contribution
It presents new examples of noncommutative spheres with 'easy' quantum isometry groups and discusses broader axiomatization issues in noncommutative geometry.
Findings
Half-liberated sphere and free sphere are introduced.
These spheres have 'easy' quantum isometry groups.
Discussion on axiomatization and non-easy cases.
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.
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