Affiliation:
1. Department of Mathematics, University at Buffalo, Buffalo, NY 14260-2900, USA
Abstract
Abstract
We introduce the coherent algebra of a compact metric measure space by analogy with the corresponding concept for a finite graph. As an application we show that upon topologizing the collection of isomorphism classes of compact metric measure spaces appropriately, the subset consisting of those with trivial compact quantum automorphism group is of 2nd Baire category. The latter result can be paraphrased as saying that “most” compact metric measure spaces have no (quantum) symmetries; in particular, they also have trivial ordinary (i.e., classical) automorphism group.
Funder
National Science Foundation
Publisher
Oxford University Press (OUP)
Reference18 articles.
1. An invitation to C-algebras;Averson,1976
2. Quantum isometry groups of 0-dimensional manifolds;Bhowmick;Trans. Amer. Math. Soc.,2011
3. Quantum automorphism groups of finite graphs;Bichon;Proc. Am. Math. Soc,2003
4. Graduate Studies in Mathematics;Burago,2001
5. Coherent Configurations, Association Schemes and Permutation Groups;Cameron,2003
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献