| Register
\(\newcommand{\Cat}{{\rm Cat}} \) \(\newcommand{\A}{\mathcal A} \) \(\newcommand{\freestar}{ \framebox[7pt]{$\star$} }\)

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


    1. Add remark

      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.