Tracially lyriform $\mathrm{C}^*$-algebras
Bhishan Jacelon

TL;DR
This paper introduces tracially lyriform $ ext{C}^*$-algebras, extending quantum metric structures to include stronger topologies and classical Wasserstein metrics, with applications to noncommutative geometry and classification of $ ext{C}^*$-algebras.
Contribution
It develops a new category of tracially lyriform $ ext{C}^*$-algebras that generalizes quantum metric spaces and incorporates classical Wasserstein metrics, enhancing the framework for classifiable $ ext{C}^*$-algebras.
Findings
Constructed examples from fractals and Alexandrov spaces.
Established behavior under inductive limits.
Analyzed geometry and statistics of embedding spaces.
Abstract
Quantum metric Choquet simplices are special kinds of compact quantum metric spaces designed for distance measurement in and around the category of stably finite Elliott-classifiable -algebras. The primary objective of this article is to introduce versions of these structures for which the associated tracial metrics need not be induced by Lipschitz seminorms and may induce strictly stronger topologies than the weak-topology. The resulting category of 'tracially lyriform -algebras' behaves well with respect to sequential inductive limits and accommodates the full family of classical -Wasserstein metrics on probability spaces, including . Examples of projectionless, classifiable tracial Wasserstein spaces are built as noncommutative spaces of observables of certain compact length spaces, including: fractals like the Sierpi\'nski gasket, the…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Operator Algebra Research · Noncommutative and Quantum Gravity Theories · Random Matrices and Applications
