Frobenius induction for algebras

TL;DR

This paper explores the induction process of algebras in the context of Hopf algebra homomorphisms, connecting different induction methods inspired by finite group representation theory, with broader applicability.

Contribution

It establishes a link between two induction procedures for algebras over Hopf algebras, extending concepts from finite group theory to more general algebraic contexts.

Findings

Connection between two induction methods for algebras over Hopf algebras.

Generalization of finite group representation concepts.

Applicability to broader algebraic structures.

Abstract

Let $B\rightarrow A$ be a homomorphism of Hopf algebras and let $C$ be an algebra. We consider the induction from $B$ to $A$ of $C$ in two cases: when $C$ is a $B$-interior algebra and when $C$ is a $B$-module algebra. Our main results establish the connection between the two inductions. The inspiration comes from finite group representation theory, and some constructions work in even more general contexts.