On the composition product of saturated fusion systems
Sejong Park, K\'ari Ragnarsson, Radu Stancu
TL;DR
This paper explores how the composition product of saturated fusion systems relates to their characteristic idempotents, providing a framework for understanding transfer compatibility in such systems.
Contribution
It establishes a relationship between the characteristic idempotent of a composition product and those of its component systems, advancing the theory of fusion systems.
Findings
Relationship between characteristic idempotents established
Transfer compatibility results derived
Framework for composition products in saturated fusion systems
Abstract
We say that a fusion system is the composition product of two subsystems if every morphism can be factored as a morphism in one fusion system followed by a morphism in the other. We establish a relationship between the characteristic idempotent of a saturated fusion system that is the composition product of saturated subsystems and the characteristic idempotents of the component systems. Consequently we obtain a compatibility result for transfer through the composition product and transfer through the component systems.
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.