Finite Block Theory and Hopf Algebra Actions

A ring is said to have finite block theory if it can be written as the finite direct sum of indecomposable subrings. In the paper, algebras R are acted on by Hopf algebras H. We prove a series of going up and going down results analyzing when R and its subalgebra of invariants R ^H have finite block theory. We also provide counterexamples when the hypotheses of our main results are weakened. Presented by D. Passman