Representations and almost split sequences for Hopf algebras

General properties of finite dimensional Hopf algebras are investigated. In particular, we generalize some of the work on almost split sequences of Auslander and Carlson on group rings to (not necessarily cocommutative) Hopf algebras with involutive antipode. We also give a new proof of a theorem of Larson, [2], which says that for a finite dimensional Hopf algebra having involutive antipode, if the algebra is not semisimple, then the dimension of any finitely generated projective module is not invertible in the field