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Selflessness, MIF and opposition in groups acting on exotic buildings

Corentin Le Bars, Elyasheev Leibtag, Itamar Vigdorovich

math.GRarXiv:2609.17129

Abstract

We prove that groups acting freely and cocompactly on (possibly exotic) affine buildings of type A2 and C2 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.

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