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

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

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...

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Бібліографічні деталі
Дата:	2025
Автор:	Guédénon, Thomas
Формат:	Стаття
Мова:	English
Опубліковано:	Lugansk National Taras Shevchenko University 2025
Теми:	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
Онлайн доступ:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2345
Теги:	Додати тег Немає тегів, Будьте першим, хто поставить тег для цього запису!
Назва журналу:	Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics

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Резюме:	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 Theorem of $(A,H)$-Hopf modules to $(A,{\mathcal G},H)$-comodules, and we deduce relative projectivity in the category of $(A,{\mathcal G},H)$-comodules. In many applications, $A$ could be a commutative $G$-graded $\mathcal G$-module algebra, where $G$ is an abelian group and $\mathcal G$ is a $G$-graded Lie algebra; or a rational $({\mathcal G},G)$-module algebra, where $G$ is an affine algebraic group and $\mathcal G$ is a rational $G$-module Lie algebra.

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

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