Induction and coinduction for Hopf algebras: Applications
Let \(H\) be a finite dimensional and semisimple Hopf algebra, and \(A\) an \(H\)-module algebra. The authors study the induced and coinduced functors from the ring of invariants of \(A\) and show, in analogy with Theorem 1.1 of \textit{C. Năstăsescu} [J. Algebra 120, 119-138 (1989; Zbl 0678.16001)] that they arise in adjoint pairs. This result is subsequently applied to Clifford theory, and also to give a description of injective envelopes in the category of modules over the smash product \(A\# H\). In the last part a similar result is obtained for induction and coinduction from semi-invariants.
scientific article; zbMATH DE number 589936