17.108 (2010)
SolvedIs the group $\langle a, b, t \mid a^t = ab, b^t = ba \rangle$ linear?
If not, this would be an easy example of a non-linear hyperbolic group.
Progress
Yes, this group is linear. Indeed, as noticed by M. Sapir, this group is the mapping torus of an irreducible atoroidal self-monomorphism of a free group; thus it is virtually special, and hence $\mathbb{Z}$-linear by Theorem B in (M. F. Hagen, D. T. Wise, Duke Math. J., 165, no. 9 (2016), 1753–1813). (M. F. Hagen, Letter of 6 August 2018.)
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