$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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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

id	oai:ojs.admjournal.luguniv.edu.ua:article-2345
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spelling	oai:ojs.admjournal.luguniv.edu.ua:article-23452025-10-27T20:24:52Z Fundamental theorem of $(A,\mathcal G,H)$-comodules Guédénon, Thomas 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 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. Lugansk National Taras Shevchenko University 2025-10-27 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2345 10.12958/adm2345 Algebra and Discrete Mathematics; Vol 40, No 1 (2025) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2345/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2345/1260 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2345/1269 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2345/1270 Copyright (c) 2025 Algebra and Discrete Mathematics
institution	Algebra and Discrete Mathematics
baseUrl_str
datestamp_date	2025-10-27T20:24:52Z
collection	OJS
language	English
topic	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
spellingShingle	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 Guédénon, Thomas Fundamental theorem of $(A,\mathcal G,H)$-comodules
topic_facet	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
format	Article
author	Guédénon, Thomas
author_facet	Guédénon, Thomas
author_sort	Guédénon, Thomas
title	Fundamental theorem of $(A,\mathcal G,H)$-comodules
title_short	Fundamental theorem of $(A,\mathcal G,H)$-comodules
title_full	Fundamental theorem of $(A,\mathcal G,H)$-comodules
title_fullStr	Fundamental theorem of $(A,\mathcal G,H)$-comodules
title_full_unstemmed	Fundamental theorem of $(A,\mathcal G,H)$-comodules
title_sort	fundamental theorem of $(a,\mathcal g,h)$-comodules
description	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.
publisher	Lugansk National Taras Shevchenko University
publishDate	2025
url	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2345
work_keys_str_mv	AT guedenonthomas fundamentaltheoremofamathcalghcomodules
first_indexed	2025-10-26T02:08:37Z
last_indexed	2025-10-28T02:44:43Z
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Fundamental theorem of \((A,\mathcal G,H)\)-comodules

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