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arXiv · 2202.04714

Crossed Product Equivalence of Quantum Automorphism Groups

Michael Brannan·Floris Elzinga·Samuel J. Harris·Makoto Yamashita
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Abstract

We compare the algebras of the quantum automorphism group of finite-dimensional C$^\ast$-algebra $B$, which includes the quantum permutation group $S_N^+$, where $N = \dim B$. We show that matrix amplification and crossed products by trace-preserving actions by a finite Abelian group $\Gamma$ lead to isomorphic $\ast$-algebras. This allows us to transfer various properties such as inner unitarity, Connes embeddability, and strong $1$-boundedness between the various algebras associated with these quantum groups.

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Michael Brannan, Floris Elzinga, Samuel J. Harris, Makoto Yamashita. 2022-02-09. Crossed Product Equivalence of Quantum Automorphism Groups. https://arxiv.org/abs/2202.04714

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