  This paper considers an invariant of modules over a finite-dimensional Hopf
algebra, called the critical group. This generalizes the critical groups of
complex finite group representations studied by Benkart, Klivans, Reiner and
Gaetz. A formula is given for the cardinality of the critical group generally,
and the critical group for the regular representation is described completely.
A key role in the formulas is played by the greatest common divisor of the
dimensions of the indecomposable projective representations.
