  We begin the study of PBW deformations of graded algebras relevant to the
theory of Hopf algebras. One of our examples is the Fomin-Kirillov algebra FK3.
Another one appeared in a paper of Garc\'ia Iglesias and Vay. As a consequence
of our methods, we determine when the deformations are semisimple and we are
able to produce PBW bases and polynomial identities for these deformations.
