  We find particular relations which we call "Bernoulli-type" in some
noncommutative polynomial ring with a single nontrivial relation. More
precisely, our ring is isomorphic to the universal enveloping algebra of a
two-dimensional non-abelian Lie algebra. From these Bernoulli-type relations in
our ring, we can obtain a representation on a certain left ideal with the
Bernoulli numbers as structure constants.
