Some Remarks on the Braided Thompson Group BV
  Matthew Brin and Patrick Dehornoy independently discovered a braided version BV of Thompson's group V. In this paper, we discuss some properties of BV that might make the group interesting for group based cryptography. In particular, we show that BV does not admit a non-trivial linear representation. 
Kai-Uwe Bux, Dmitriy Sonkin