Fundamental theorem of \((A,\mathcal G,H)\)-comodules

• Date: 2025
• Main Author: Guédénon, Thomas
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2025
• Subjects: Lie algebra; module over a Lie algebra; Hopf algebra; Hopf module; \(H\)-comodule Lie algebra; \(({\mathcal G},H)\)-comodule algebra; \((A,{\mathcal G},H)\)-comodule; Primary: 16T05. Secondary: 17B60
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2345
• Journal Title: Algebra and Discrete Mathematics

Let \(k\) be a field, \(H\) a Hopf algebra with a bijective antipode, \(\mathcal G\) an \(H\)-comodule Lie algebra and \(A\) a commutative \(({\mathcal G},H)\)-comodule algebra. We assume that there is an \(H\)-colinear algebra map from \(H\) to \(A^{\mathcal G}\). We generalize the Fundamental Theo...