Infinite dimensional linear groups with a spacious family of $G$-invariant subspaces

Let $F$ be a field, $A$ be a vector space over $F$, $GL (F, A)$ be the group of all automorphisms of the vector space $A$. If $B leq A$ then denote by $mathop{m Core}_G (B)$ the largest $G$-invariant subspace of~$B$. A subspace $B$ is called almost $G$-invariant if $mathop{m dim}_F (B/mathop{m Core}...

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Main Author: A. V. Sadovnichenko
Format: Article
Language:deu
Published: Ivan Franko National University of Lviv 2013-10-01
Series:Математичні Студії
Subjects:
Online Access:http://matstud.org.ua/texts/2013/40_1/11-15.pdf
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author A. V. Sadovnichenko
author_facet A. V. Sadovnichenko
author_sort A. V. Sadovnichenko
collection DOAJ
description Let $F$ be a field, $A$ be a vector space over $F$, $GL (F, A)$ be the group of all automorphisms of the vector space $A$. If $B leq A$ then denote by $mathop{m Core}_G (B)$ the largest $G$-invariant subspace of~$B$. A subspace $B$ is called almost $G$-invariant if $mathop{m dim}_F (B/mathop{m Core}_G (B))$ is finite. In this paper we described the {case where} every subspace of $A$ is almost $G$-invariant.
format Article
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publishDate 2013-10-01
publisher Ivan Franko National University of Lviv
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series Математичні Студії
spelling doaj-art-3fb1b9abbe7e4caba1bbc2d3eadbd9382025-08-20T03:15:43ZdeuIvan Franko National University of LvivМатематичні Студії1027-46342013-10-014011115Infinite dimensional linear groups with a spacious family of $G$-invariant subspacesA. V. SadovnichenkoLet $F$ be a field, $A$ be a vector space over $F$, $GL (F, A)$ be the group of all automorphisms of the vector space $A$. If $B leq A$ then denote by $mathop{m Core}_G (B)$ the largest $G$-invariant subspace of~$B$. A subspace $B$ is called almost $G$-invariant if $mathop{m dim}_F (B/mathop{m Core}_G (B))$ is finite. In this paper we described the {case where} every subspace of $A$ is almost $G$-invariant.http://matstud.org.ua/texts/2013/40_1/11-15.pdfvector spacelinear groupmodule$G$-invariant subspacealmost invariant subspace
spellingShingle A. V. Sadovnichenko
Infinite dimensional linear groups with a spacious family of $G$-invariant subspaces
Математичні Студії
vector space
linear group
module
$G$-invariant subspace
almost invariant subspace
title Infinite dimensional linear groups with a spacious family of $G$-invariant subspaces
title_full Infinite dimensional linear groups with a spacious family of $G$-invariant subspaces
title_fullStr Infinite dimensional linear groups with a spacious family of $G$-invariant subspaces
title_full_unstemmed Infinite dimensional linear groups with a spacious family of $G$-invariant subspaces
title_short Infinite dimensional linear groups with a spacious family of $G$-invariant subspaces
title_sort infinite dimensional linear groups with a spacious family of g invariant subspaces
topic vector space
linear group
module
$G$-invariant subspace
almost invariant subspace
url http://matstud.org.ua/texts/2013/40_1/11-15.pdf
work_keys_str_mv AT avsadovnichenko infinitedimensionallineargroupswithaspaciousfamilyofginvariantsubspaces