Year: 2026
Type: preprint
Abstract: We introduce the Hopf image of a right coaction of a Hopf algebra on an algebra as the smallest Hopf subalgebra through which the coaction factors. We establish its basic properties and show that the induced coaction on the Hopf image is inner-faithful. For coactions on Nichols algebras arising from Yetter--Drinfeld modules, we prove that the Hopf image is the smallest Hopf subalgebra detected by the underlying coaction on the Yetter--Drinfeld module. We give explicit examples of proper non-trivial Hopf images arising from bosonizations.
Source: arXiv (Cornell University)
Author: Bhattacharjee, Arnab
Institution: Charles University
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213611414