Hopf images in locally compact quantum groups
Abstract
This manuscript is devoted to the study of the concept of a generating subset (a.k.a. Hopf image of a morphism) in the setting of locally compact quantum groups. The aim of this paper is to provide an accurate description of the Hopf image of a given morphism. We extend and unify the previously existing approaches for compact and discrete quantum groups and present some results that can shed light on some local perspective in the theory of quantum groups. In particular, we provide a characterization of fullness of Hopf image in the language of partial actions as well as in representation-theoretic terms in the spirit of representation -categories, extending some known results not only to the broader setting of non-compact quantum groups, but also encompassing a broader setting of generating subsets.
Cite
@article{arxiv.1611.06225,
title = {Hopf images in locally compact quantum groups},
author = {Paweł Józiak and Paweł Kasprzak and Piotr M. Sołtan},
journal= {arXiv preprint arXiv:1611.06225},
year = {2017}
}
Comments
v1: 21 pages, 2 tikz diagrams v2: 23 pages, 2 tikz diagrams. Added Section 7 with examples; several details expanded and some typos corrected. Bibliography updated