A note on the non-abelian tensor squares of linear groups

Abstract

We show that there exists a finitely generated linear group whose non-abelian tensor square is not linear. On the other hand, the non-abelian tensor square of the braid group $B_n$, $n>3$, is linear.

The main example and some of the initial ideas were generated with the assistance of AI. The arguments were subsequently checked and substantially simplified by the author. Whether the resulting note will ultimately be submitted for publication remains, at present, an entirely human uncertainty