Finite Hopf Integrals, Frobenius Duality, and Maschke — Examples

Recover the finite-group Maschke characteristic condition from Σg, compute Taft integrals and failure of semisimplicity, and verify the Frobenius pairing in H4. Do not infer semisimplicity of H* or S²=id in arbitrary characteristic from this theorem.

These are planned worked examples and counterexamples for finite-hopf-integrals-frobenius-duality-and-maschke, with empty item lists pending normal authoring and proof review. Each example must calculate from the stated hypotheses, and each counterexample must verify both its premises and the failed conclusion. This companion is a dependency leaf and supplies no theorem to another page.