  Dosi and, quite recently, the author showed that, on the character space of a
nilpotent Lie algebra, there exists a sheaf of Fr\'echet--Arens--Michael
algebras (of noncommutative holomorphic functions in the complex case and of
noncommutative smooth functions in the real case). We construct similar sheaves
(both versions, holomorphic and smooth) on a special space of representations
for the Lie algebra of the group of affine transformations of the real line
(which is the simplest nonnilpotent solvable Lie algebra).
