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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Ivan Franko National University of Lviv
2013-10-01
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| Series: | Математичні Студії |
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| 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 |
| id | doaj-art-3fb1b9abbe7e4caba1bbc2d3eadbd938 |
| institution | DOAJ |
| issn | 1027-4634 |
| language | deu |
| publishDate | 2013-10-01 |
| publisher | Ivan Franko National University of Lviv |
| record_format | Article |
| 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 |