  The Jacobian group (also called the sandpile group, Picard group, or critical
group) of a graph or, more generally, of a regular matroid has been well
studied. Sixth-root-of-unity matroids, also called complex unimodular matroids,
are generalizations of regular matroids. This paper provides a definition, and
establishes some basic properties, of the Jacobian group of a
sixth-root-of-unity matroid.
