Projectivity and flatness over the graded ring of normalizing elements

Let $k$ be a field, $H$ a cocommutative bialgebra, $A$ a commutative left $H$-module algebra, $Hom(H,A)$ the $k$-algebra of the $k$-linear maps from $H$ to $A$ under the convolution product, $Z(H,A)$ the submonoid of $Hom(H,A)$ whose elements satisfy the cocycle condition and \(G...

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Datum:	2015
1. Verfasser:	Guédénon, T.
Format:	Artikel
Sprache:	English
Veröffentlicht:	Lugansk National Taras Shevchenko University 2015
Schlagworte:	projective module flat module bialgebra smash product graded ring normalizing element weakly semi-invariant element 16D40 16W50 16W30
Online Zugang:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/44
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Назва журналу:	Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics

id	admjournalluguniveduua-article-44
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spelling	admjournalluguniveduua-article-442015-09-28T11:22:08Z Projectivity and flatness over the graded ring of normalizing elements Guédénon, T. projective module, flat module, bialgebra, smash product, graded ring, normalizing element, weakly semi-invariant element 16D40, 16W50, 16W30 Let $k$ be a field, $H$ a cocommutative bialgebra, $A$ a commutative left $H$-module algebra, $Hom(H,A)$ the $k$-algebra of the $k$-linear maps from $H$ to $A$ under the convolution product, $Z(H,A)$ the submonoid of $Hom(H,A)$ whose elements satisfy the cocycle condition and $G$ any subgroup of the monoid $Z(H,A)$. We give necessary and sufficient conditions for the projectivity and flatness over the graded ring of normalizing elements of $A$. When $A$ is not necessarily commutative we obtain similar results over the graded ring of weakly semi-invariants of $A$ replacing $Z(H,A)$ by the set $\chi(H,Z(A)^H)$ of all algebra maps from $H$ to $Z(A)^H$, where $Z(A)$ is the center of $A$. Lugansk National Taras Shevchenko University 2015-09-28 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/44 Algebra and Discrete Mathematics; Vol 19, No 2 (2015) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/44/11 Copyright (c) 2015 Algebra and Discrete Mathematics
institution	Algebra and Discrete Mathematics
baseUrl_str
datestamp_date	2015-09-28T11:22:08Z
collection	OJS
language	English
topic	projective module flat module bialgebra smash product graded ring normalizing element weakly semi-invariant element 16D40 16W50 16W30
spellingShingle	projective module flat module bialgebra smash product graded ring normalizing element weakly semi-invariant element 16D40 16W50 16W30 Guédénon, T. Projectivity and flatness over the graded ring of normalizing elements
topic_facet	projective module flat module bialgebra smash product graded ring normalizing element weakly semi-invariant element 16D40 16W50 16W30
format	Article
author	Guédénon, T.
author_facet	Guédénon, T.
author_sort	Guédénon, T.
title	Projectivity and flatness over the graded ring of normalizing elements
title_short	Projectivity and flatness over the graded ring of normalizing elements
title_full	Projectivity and flatness over the graded ring of normalizing elements
title_fullStr	Projectivity and flatness over the graded ring of normalizing elements
title_full_unstemmed	Projectivity and flatness over the graded ring of normalizing elements
title_sort	projectivity and flatness over the graded ring of normalizing elements
description	Let $k$ be a field, $H$ a cocommutative bialgebra, $A$ a commutative left $H$-module algebra, $Hom(H,A)$ the $k$-algebra of the $k$-linear maps from $H$ to $A$ under the convolution product, $Z(H,A)$ the submonoid of $Hom(H,A)$ whose elements satisfy the cocycle condition and $G$ any subgroup of the monoid $Z(H,A)$. We give necessary and sufficient conditions for the projectivity and flatness over the graded ring of normalizing elements of $A$. When $A$ is not necessarily commutative we obtain similar results over the graded ring of weakly semi-invariants of $A$ replacing $Z(H,A)$ by the set $\chi(H,Z(A)^H)$ of all algebra maps from $H$ to $Z(A)^H$, where $Z(A)$ is the center of $A$.
publisher	Lugansk National Taras Shevchenko University
publishDate	2015
url	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/44
work_keys_str_mv	AT guedenont projectivityandflatnessoverthegradedringofnormalizingelements
first_indexed	2025-12-02T15:44:34Z
last_indexed	2025-12-02T15:44:34Z
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Projectivity and flatness over the graded ring of normalizing elements

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