Work

Selflessness, MIF and opposition in groups acting on exotic buildings

Year: 2026

Type: preprint

Abstract: We prove that groups acting freely and cocompactly on (possibly exotic) affine buildings of type $\tilde{A}_2$ and $\tilde C_2$ are mixed-identity free and have selfless reduced $C^*$-algebras. These results follow from a strong form of ping-pong dynamics that we call 'transversal contractivity'. Our main geometric result regards domesticity properties of elements in the associated polygons at infinity: we prove that, in our context, the opposite geometry of a hyperbolic element is topologically large.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.17129

Authors: Bars, Corentin Le, Leibtag, Elyasheev, Vigdorovich, Itamar

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7213407032

Cites:

Cited by: 1

Related to: 10