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1. Positive elements that aren’t sums of squares in group algebra


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      Problem 1.1.

      [William Slofstra] Find a positive element of \mathbb{C}[\mathbb{F}_n\times \mathbb{F}_n] – the group algebra of the product of the free group with itself – that is not a sum of squares. Here, positive means positive in all Hilbert space representations. The problem is known for n=2 so the general case is n\geq 3.

          Cite this as: AimPL: Noncommutative inequalities, available at http://aimpl.org/noncommineqV.