The ℓ¹-Bass conjecture for all discrete groups

Proves the ℓ¹-Bass conjecture for every discrete group: Hattori–Stallings traces of idempotent matrices over \ell^1(G) are supported on finitely many finite-order conjugacy classes. The algebraic companion proves the integral Bass trace conjecture and Kaplansky's idempotent conjecture for torsion-free groups over every commutative unital characteristic-zero domain. (Lean)

Manuscripts (2)

The ℓ¹-Bass Conjecture for Discrete Groups

October 5, 2026 · source · cite as \cite{OAI:The-l1-Bass-Conjecture-for-Discrete-Groups-October-5-2026}

We prove the ℓ¹-Bass conjecture for every discrete group. The Hattori–Stallings trace of every idempotent matrix over the complex ℓ¹ group algebra is supported on finitely many conjugacy classes of finite-order elements.

The Bass trace conjecture and the characteristic-zero Kaplansky idempotent conjecture

September 24, 2026 · source · Lean formalization available · cite as \cite{OAI:The-Bass-trace-conjecture-for-complex-group-rings-September-24-2026}

We prove the complex group-ring Bass trace conjecture for every discrete group: the Hattori–Stallings trace of a finitely generated projective module over its complex group ring is supported on conjugacy classes of finite-order elements. As a consequence, for every torsion-free group G and every commutative unital domain R of characteristic zero, the only idempotents in RG are 0 and 1. This proves Kaplansky's idempotent conjecture in characteristic zero.

Result 207 · Algebra. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.