Non-commutative classifying spaces of groups via quasi-topologies and pro-$C^*$-algebras

Alexandru Chirvasitu; Mariusz Tobolski

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arXiv · 2304.14681

Non-commutative classifying spaces of groups via quasi-topologies and pro-$C^*$-algebras

Alexandru Chirvasitu·Mariusz Tobolski

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Abstract

For a locally compact Hausdorff topological group $G$, we construct a universal pro-$C^*$-algebra $C(E^+G)$ as the non-commutative geometer's analogue of the total space $EG$ of the classifying principal $G$-bundle $EG\to BG$. The pro-$C^*$-algebra $C(EG)$ of (possibly unbounded) continuous functions on $EG$ is then recoverable as the abelianization of $C(E^+G)$. Along the way, we develop various aspects of the theory of quasi-topological $G$-spaces and $G$-pro-$C^*$-algebras.

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BibTeX RIS

Alexandru Chirvasitu, Mariusz Tobolski. 2023-04-28. Non-commutative classifying spaces of groups via quasi-topologies and pro-$C^*$-algebras. https://arxiv.org/abs/2304.14681

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