19.9 (2018)

Let $G$ be a finitely generated linear group.
$\qquad$ a) Is it true that the non-abelian tensor square $G \otimes G$ is a linear group?
$\qquad$ b) In particular, is this true for the braid group $B_n$ for $n > 3$?

It is known that $B_3 \otimes B_3$ is linear, and there is a countable group $G$ such that $G \otimes G$ is not linear. See the definition of the non-abelian tensor square in (R. Brown, J.-L. Loday, Topology, 26, no. 3 (1987), 311–335).