Papers › Noncommutative real algebraic geometry of Kazhdan's property (T)
Noncommutative real algebraic geometry of Kazhdan's property (T)
Narutaka Ozawa
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
It is well-known that a finitely generated group Γ has Kazhdan's property (T) if and only if the Laplacian element Δ in ℝ[Γ] has a spectral gap. In this paper, we prove that this phenomenon is witnessed in ℝ[Γ]. Namely, Γ has property (T) if and only if there are a constant κ>0 and a finite sequence ξ₁,...,ξₙ in ℝ[Γ] such that Δ²-κΔ= ∑ᵢ ξᵢ^*ξᵢ. This result suggests the possibility of finding new examples of property (T) groups by solving equations in ℝ[Γ], possibly with an assist of computers.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections