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Open problem: Construct a non-hyperlinear group

A positive resolution to Connes' embedding problem would've implied that all countable discrete groups are hyperlinear. Since MIP*=RE gives a negative answer to CEP, this leaves open the possibility that there are non-hyperlinear groups.

One approach to this is to create a linear constraint system (LCS) game $G$ whose commuting operator value $\omega^{co}(G)$ is different from its tensor product value $\omega^*(G)$.

Thus, can the separating nonlocal game constructed in the MIP*=RE paper be formulated as a linear constraint system game?

hyperlinear.txt · Last modified: 2020/08/28 15:54 by admin