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

Alexandru Chirvasitu; Mariusz Tobolski

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

Operator Algebras 2023-05-01 v1 Algebraic Topology Category Theory Functional Analysis Quantum Algebra

Authors: Alexandru Chirvasitu , Mariusz Tobolski

Abstract

For a completely Hausdorff quasi-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.

Keywords

quasi-topological group classifying space pro-c*-algebra non-commutative geometry g-space principal bundle

Cite

@article{arxiv.2304.14681,
  title  = {Non-Commutative classifying spaces of groups via quasi-topologies and pro-$C^*$-algebras},
  author = {Alexandru Chirvasitu and Mariusz Tobolski},
  journal= {arXiv preprint arXiv:2304.14681},
  year   = {2023}
}

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33 pages + references

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

Abstract

Keywords

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