  Motivated by the structure of the uniform posets we introduce the notion of
an augmented down-up (or ADU) algebra. We discuss how ADU algebras are related
to the down-up algebras defined by Benkart and Roby. For each ADU algebra we
give two presentations by generators and relations. We also display a
$Z$-grading and a linear basis. In addition we show that the center is
isomorphic to a polynomial algebra in two variables. We display seven families
of uniform posets and show that each gives an ADU algebra module in a natural
way. The main inspiration for the ADU algebra concept comes from the second
author's thesis concerning a type of uniform poset constructed using a dual
polar graph.
