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Triangular matrix categories over quasi-hereditary categories
In this paper, we prove that the lower triangular matrix category $\Lambda =\left [ \begin{smallmatrix} \mathcal{T}&0\\ M&\mathcal{U} \end{smallmatrix} \right ]$ , where $\mathcal{T}$ and $\mathcal{U}$ are $\textrm{Hom}$ -finite, Krull–Schmidt $K$ -quasi-hereditary categories and $M$ is an $...
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| Published in: | Glasgow mathematical journal 2024-09, Vol.66 (3), p.449-470 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c269t-caabd89e2b7d70686ce8379267712ab412dbf42bbed67e01e6efc1ca7a6591f3 |
| container_end_page | 470 |
| container_issue | 3 |
| container_start_page | 449 |
| container_title | Glasgow mathematical journal |
| container_volume | 66 |
| creator | Ochoa De La Cruz, Rafael Francisco Ortíz Morales, Martin Santiago Vargas, Valente |
| description | In this paper, we prove that the lower triangular matrix category
$\Lambda =\left [ \begin{smallmatrix} \mathcal{T}&0\\ M&\mathcal{U} \end{smallmatrix} \right ]$
, where
$\mathcal{T}$
and
$\mathcal{U}$
are
$\textrm{Hom}$
-finite, Krull–Schmidt
$K$
-quasi-hereditary categories and
$M$
is an
$\mathcal{U}\otimes _K \mathcal{T}^{op}$
-module that satisfies suitable conditions, is quasi-hereditary. This result generalizes the work of B. Zhu in his study on triangular matrix algebras over quasi-hereditary algebras. Moreover, we obtain a characterization of the category of the
$_\Lambda \Delta$
-filtered
$\Lambda$
-modules. |
| doi_str_mv | 10.1017/S0017089524000053 |
| format | article |
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$\Lambda =\left [ \begin{smallmatrix} \mathcal{T}&0\\ M&\mathcal{U} \end{smallmatrix} \right ]$
, where
$\mathcal{T}$
and
$\mathcal{U}$
are
$\textrm{Hom}$
-finite, Krull–Schmidt
$K$
-quasi-hereditary categories and
$M$
is an
$\mathcal{U}\otimes _K \mathcal{T}^{op}$
-module that satisfies suitable conditions, is quasi-hereditary. This result generalizes the work of B. Zhu in his study on triangular matrix algebras over quasi-hereditary algebras. Moreover, we obtain a characterization of the category of the
$_\Lambda \Delta$
-filtered
$\Lambda$
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$\Lambda =\left [ \begin{smallmatrix} \mathcal{T}&0\\ M&\mathcal{U} \end{smallmatrix} \right ]$
, where
$\mathcal{T}$
and
$\mathcal{U}$
are
$\textrm{Hom}$
-finite, Krull–Schmidt
$K$
-quasi-hereditary categories and
$M$
is an
$\mathcal{U}\otimes _K \mathcal{T}^{op}$
-module that satisfies suitable conditions, is quasi-hereditary. This result generalizes the work of B. Zhu in his study on triangular matrix algebras over quasi-hereditary algebras. Moreover, we obtain a characterization of the category of the
$_\Lambda \Delta$
-filtered
$\Lambda$
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$\Lambda =\left [ \begin{smallmatrix} \mathcal{T}&0\\ M&\mathcal{U} \end{smallmatrix} \right ]$
, where
$\mathcal{T}$
and
$\mathcal{U}$
are
$\textrm{Hom}$
-finite, Krull–Schmidt
$K$
-quasi-hereditary categories and
$M$
is an
$\mathcal{U}\otimes _K \mathcal{T}^{op}$
-module that satisfies suitable conditions, is quasi-hereditary. This result generalizes the work of B. Zhu in his study on triangular matrix algebras over quasi-hereditary algebras. Moreover, we obtain a characterization of the category of the
$_\Lambda \Delta$
-filtered
$\Lambda$
-modules.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/S0017089524000053</doi><tpages>22</tpages></addata></record> |
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| identifier | ISSN: 0017-0895 |
| ispartof | Glasgow mathematical journal, 2024-09, Vol.66 (3), p.449-470 |
| issn | 0017-0895 1469-509X |
| language | eng |
| recordid | cdi_proquest_journals_3131719306 |
| source | Cambridge Journals Online |
| subjects | Categories Modules |
| title | Triangular matrix categories over quasi-hereditary categories |
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