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Some interactions between Hopf Galois extensions and noncommutative rings

Authors :
Armando Reyes
Fabio Calderón
Source :
Universitas Scientiarum, Vol 27, Iss 2, Pp 58-161 (2022)
Publication Year :
2022
Publisher :
Pontificia Universidad Javeriana, 2022.

Abstract

In this paper, our objects of interest are Hopf Galois extensions (e.g., Hopf algebras, Galois field extensions, strongly graded algebras, crossed products, principal bundles, etc.) and families of noncommutative rings (e.g., skew polynomial rings, PBW extensions and skew PBW extensions, etc.) We collect and systematize questions, problems, properties and recent advances in both theories by explicitly developing examples and doing calculations that are usually omitted in the literature. In particular, for Hopf Galois extensions we consider approaches from the point of view of quantum torsors (also known as quantum heaps) and Hopf Galois systems, while for some families of noncommutative rings we present advances in the characterization of ring-theoretic and homological properties. Every developed topic is exemplified with abundant references to classic and current works, so this paper serves as a survey for those interested in either of the two theories. Throughout, interactions between both are presented.

Details

Language :
English, Spanish; Castilian
ISSN :
01227483 and 20271352
Volume :
27
Issue :
2
Database :
Directory of Open Access Journals
Journal :
Universitas Scientiarum
Publication Type :
Academic Journal
Accession number :
edsdoj.0559d87c546f4c889906318ad9a75448
Document Type :
article
Full Text :
https://doi.org/10.11144/Javeriana.SC271.sibh