  In this paper we generalize some classical birational transformations to the
non-commutative case. In particular we show that 3-dimensional quadratic
Sklyanin algebras (non-commutative projective planes) and 3-dimensional cubic
Sklyanin algebras (non-commutative quadrics) have the same function field. In
the same vein we construct and analogue of the Cremona transform for
non-commutative projective planes.
