OpenAI reports the ℓ¹-Bass conjecture for every discrete group

For every discrete group G, the Hattori–Stallings trace of every idempotent matrix over the complex Banach algebra ℓ¹(G) has finite support, contained in conjugacy classes of finite-order elements.

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Understanding the problem

Read the background

For every discrete group G, the Hattori–Stallings trace of every idempotent matrix over the complex Banach algebra ℓ¹(G) has finite support, contained in conjugacy classes of finite-order elements.

Why it matters

If correct, resolves the ℓ¹-Bass conjecture for arbitrary discrete groups.

What counts as progress

Does the Hattori–Stallings trace of every ℓ¹(G) idempotent have finite torsion-class support for arbitrary G?

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