A Skolem-Noether theorem for coalgebra measurings
The main theorem of this paper is: Theorem. Let A be a central simple Artinian algebra over a field k, B a finite-dimensional simple subalgebra, and C a k-coalgebra measuring B to A. Assume further that for any simple subcoalgebra D of C, \(B\otimes (D^*)^{op}\) is a simple algebra. Then the measuring is A-inner. This theorem is a true generalization of the classical Skolem-Noether theorem and also implies Jacobson's theorem on inner derivations. The key step in the proof is to show that if A is injective as a (B,A)-bimodule, then if the measuring restricted to the coradical of C is inner, then the measuring is inner.
scientific article; zbMATH DE number 4208320