Fixed-point permanence under actions by finite quantum groups

Alexandru Chirvasitu

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arXiv · 2504.14579

Fixed-point permanence under actions by finite quantum groups

Alexandru Chirvasitu

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Abstract

Given an action by a finite quantum group $\mathbb{G}$ on a von Neumann algebra $M$, we prove that a number of familiar $W^*$ properties are equivalent for $M$ and the fixed-point algebra $M^{\mathbb{G}}$ (i.e. hold or not simultaneously for the two algebras); these include being hyperfinite, atomic, diffuse and of type $I$, $II$ or $III$. Moreover, in all cases the canonical central projections of $M$ and $M^{\mathbb{G}}$ cutting out the summand with the respective property coincide. The result generalizes its classical-$\mathbb{G}$ analogue due to Jones-Takesaki.

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BibTeX RIS

Alexandru Chirvasitu. 2025-04-20. Fixed-point permanence under actions by finite quantum groups. https://arxiv.org/abs/2504.14579

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