Computer proofs for Property (T), and SDP duality
Group Theory
2022-12-27 v3 Operator Algebras
Abstract
We show that the semidefinite programs involved in the computer proofs for Kazhdan's property (T) satisfy strong duality and that the dual programs have a geometric interpretation in terms of harmonic cocycles. By dualizing geometric arguments about cocycles, we are able to simplify the property (T) SDP in the case where it carries a symmetry by finite-order inner automorphisms. As an application, we simplify the SDP proof for and we prove that has property (T).
Cite
@article{arxiv.2009.05134,
title = {Computer proofs for Property (T), and SDP duality},
author = {Martin Nitsche},
journal= {arXiv preprint arXiv:2009.05134},
year = {2022}
}
Comments
one SAGE-script attached. v3: rewrite for improved presentation in the language of harmonic cocycles and simplified verification for Aut(F_4)