  In this paper we apply a method devised in \cite{HartLarsSilv1D,LarsSilv1D}
to the three-dimensional simple Lie algebra $\sll$. One of the main points of
this deformation method is that the deformed algebra comes endowed with a
canonical twisted Jacobi identity. We show in the present paper that when our
deformation scheme is applied to $\sll$ we can, by choosing parameters
suitably, deform $\sll$ into the Heisenberg Lie algebra and some other
three-dimensional Lie algebras in addition to more exotic types of algebras,
this being in stark contrast to the classical deformation schemes where $\sll$
is rigid. The resulting algebras are quadratic and we point out possible
connections to ``geometric quadratic algebras'' such as the Artin--Schelter
regular algebras, studied extensively since the beginning of the 90's in
connection with non-commutative projective geometry.
