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arXiv · 2602.06946

Symmetry of some noncommutative sphere algebras

William J. Ugalde·Joseph C. Várilly
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Abstract

Two known $q$-deformed (or `quantum') $7$-spheres, both denoted $\mathbb{S}^7_q$ in the literature, may be distinguished by the presence or absence of symmetry under $\mathrm{SU}_q(2)$. The quaternionic version of $\mathbb{S}^7_q$ has been shown by Brain and Landi to support such a symmetry. Here we show that this is not the case for the older $\mathbb{S}^7_q$ introduced by Vaksman and Soibelman: and as a consequence, these quantum $7$-spheres are not isomorphic.

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William J. Ugalde, Joseph C. Várilly. 2026-02-06. Symmetry of some noncommutative sphere algebras. https://arxiv.org/abs/2602.06946

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